MYP Standard Mathematics Topic Coordinate Geometry…

Coordinate geometry (or analytic geometry) connects algebra and geometry by describing points and shapes using coordinates and equations.
It is a foundation for building and validating mathematical models, for example when mapping locations, designing layouts, or interpreting linear data.

Coordinates Describe Location Precisely

A point on a plane is located using an ordered pair $(x,y)$.

Definition

Cartesian coordinate plane

A grid formed by two perpendicular number lines, the x-axis (horizontal) and y-axis (vertical), used to locate points with ordered pairs $(x,y)$.

The x-coordinate tells you how far left or right to move from the origin.
The y-coordinate tells you how far down or up to move.
The origin is $(0,0)$.

Because every point has a unique coordinate pair, coordinate geometry lets you calculate geometric facts (like lengths and slopes) with algebra.

Distance Between Two Points Comes From Pythagoras

Suppose you have two points $A(x_1,y_1)$ and $B(x_2,y_2)$.
If you move from $A$ to $B$, the horizontal change is $\Delta x=x_2-x_1$ and the vertical change is $\Delta y=y_2-y_1$.
Using Pythagoras' theorem on the right triangle formed by these changes gives the distance formula.

Definition

Distance formula

For points $A(x_1,y_1)$ and $B(x_2,y_2)$, the distance between them is
$$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

Why Squaring Matters

The differences $x_2-x_1$ and $y_2-y_1$ can be negative, but distance cannot be negative.
Squaring removes sign, so the formula works no matter which point you subtract first.

Common Mistake

A very common error is to forget the squares and write $\sqrt{(x_2-x_1)+(y_2-y_1)}$.
The squares are essential because the distance is based on Pythagoras.

Example question

Find the distance between $(0,0)$ and $(5,12)$.

Solution

Here, $\Delta x=5-0=5$ and $\Delta y=12-0=12$.

$$AB=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$$

Exact Form Versus Decimal Form

Sometimes you are asked to leave answers as an exact surd, such as $\sqrt{n}$, and sometimes to round to a certain number of significant figures.

Tip

To keep an exact answer, simplify inside the square root only when there is a square factor.
For example, $\sqrt{72}=\sqrt{36\cdot 2}=6\sqrt{2}$

The Midpoint Is the Average of Coordinates

The midpoint of a line segment is the point exactly halfway between the endpoints.

Definition

Midpoint formula

For endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$, the midpoint is
$$M\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$

This works because moving halfway in the $x$ direction means averaging the $x$-coordinates, and similarly for $y$.

Example question

Find the midpoint of $A(1,4)$ and $B(4,8)$.

Solution

$$M\left(\frac{1+4}{2},\frac{4+8}{2}\right)=\left(\frac{5}{2},6\right)$$

A Useful Midpoint Property

If $M$ is the midpoint of $AB$, then $AM=\tfrac12 AB$.
One way to validate this is to:
1. compute $AB$ using the distance formula,
2. compute $AM$ using the distance formula,
3. show $AM=\tfrac12 AB$.
This kind of check is an example of using logic to validate a generalization.

Active recall

For $A(a,b)$ and $B(c,d)$:

Write down the midpoint $M$.
Use the distance formula to write expressions for $AB$ and $AM$.
What changes when you compare $(c-a)$ to $\left(\tfrac{c+a}{2}-a\right)$?

Gradient Measures Steepness And Direction

A straight line's gradient (also called slope) tells how steep it is and whether it rises or falls as you move left to right.

Definition

Gradient (slope)

For two distinct points $A(x_1,y_1)$ and $B(x_2,y_2)$ on a line, the gradient is
$$m=\frac{y_2-y_1}{x_2-x_1},\quad x_2\neq x_1$$

If $m>0$, the line rises left to right.
If $m<0$, the line falls left to right.
If $m=0$, the line is horizontal.
If $x_2=x_1$, the line is vertical and the gradient is undefined.

Common Mistake

Don't swap the order in the numerator and denominator inconsistently.
If you use $(y_2-y_1)$ then you must use $(x_2-x_1)$ with the same point order.

Example question

Find the gradient of the line through $A(0,0)$ and $B(1,4)$.

Solution

$$m=\frac{4-0}{1-0}=4$$

Parallel And Perpendicular Lines Have Predictable Gradients

Gradients let you recognize angle relationships between lines without measuring angles.

Definition

Parallel lines

Two non-vertical lines are parallel if they have the same gradient.

Definition

Perpendicular lines

Two non-vertical, non-horizontal lines are perpendicular if their gradients multiply to $-1$. If one line has gradient $m\,(m\neq 0)$, then a perpendicular line has gradient $-\frac{1}{m}$.

Note

Special Cases: Horizontal And Vertical

A horizontal line has gradient $0$ and a vertical line has undefined gradient, so the "negative reciprocal" rule cannot be applied directly in that form.

A horizontal line is perpendicular to a vertical line.
Horizontal lines are parallel to each other.
Vertical lines are parallel to each other.

Hint

When checking perpendicularity, first ask: "Is one line horizontal and the other vertical?"
If yes, they are perpendicular even though gradients do not multiply neatly.

Equations Of Straight Lines Can Be Written In Different Forms

A line can be represented by an equation in several equivalent forms.
Choosing an efficient form is part of good problem solving.

Slope-Intercept Form Highlights Gradient

Definition

Slope-intercept form

The equation of a non-vertical line can be written as $$y=mx+c$$ where $m$ is the gradient and $c$ is the $y$-intercept.

Hint

The y-intercept is where the line crosses the $y$-axis, at $(0,c)$.

Point-Slope Form Is Fast When You Know A Point And The Gradient

Definition

Point-slope form

A line through $(x_1,y_1)$ with gradient $m$ can be written as $$y-y_1=m(x-x_1)$$

Note

This is often the quickest way to build an equation from a point and a gradient.

Standard Form Is Useful For Intercepts And Some Exam Requirements

Definition

Standard form (linear)

A line can be written as $$ax+by+c=0$$ with constants $a,b,c$ (often integers, and sometimes with a required sign convention such as $a>0$).

Tip

To find intercepts quickly from standard form:

y-intercept: set $x=0$ and solve for $y$.
x-intercept: set $y=0$ and solve for $x$.

Example question

Find where the line $2y-3x-7=0$ intersects the axes.

Solution

On the $y$-axis, $x=0$: $$2y-7=0\Rightarrow y=\frac{7}{2}$$
So the y-intercept is $(0,\tfrac72)$
On the $x$-axis, $y=0$: $$-3x-7=0\Rightarrow x=-\frac{7}{3}$$
So the x-intercept is $(-\tfrac73,0)$

Exam technique

If an answer is required "in the form $ax+by+c=0$ with integers", avoid fractions by multiplying through by the lowest common multiple of denominators, then rearrange so one side is 0.

Finding A Line Equation In Common Situations

Through Two Points

Find the gradient $m=\dfrac{y2-y1}{x2-x1}$.
Use point-slope form with either point.
Convert to the required form (slope-intercept or standard).

Parallel To A Given Line

Parallel lines have the same gradient.
Use the given point to find the intercept.

Example question

The line $y=px+q$ is parallel to $y=2x-6$ and passes through $(-1,7)$. Find $p$ and $q$.

Solution

Parallel means $p=2$.
Substitute the point into $y=2x+q$: $$7=2(-1)+q=-2+q\Rightarrow q=9$$
So $p=2$ and $q=9$, and the line is $y=2x+9$

Perpendicular To A Given Line

Find the gradient of the given line.
Take the negative reciprocal to get the perpendicular gradient.
Use point-slope form.

Example question

Find the equation of the line through $S(3,7)$ perpendicular to $l_2: 3x+2y+2=0$, and give it in the form $ax+by+c=0$ with $a>0$.

Solution

First rewrite $l_2$ to see its gradient: $$3x+2y+2=0\Rightarrow 2y=-3x-2\Rightarrow y=-\frac{3}{2}x-1$$
So $m_2=-\tfrac32$
A perpendicular line has gradient $$m_1=-\frac{1}{m_2}=-\frac{1}{-\tfrac32}=\frac{2}{3}$$
Use point-slope form through $(3,7)$: $$y-7=\frac{2}{3}(x-3)$$
Expand: $$y-7=\frac{2}{3}x-2\Rightarrow y=\frac{2}{3}x+5$$
Convert to standard form with integers: $$3y=2x+15\Rightarrow 2x-3y+15=0$$

Coordinate Geometry As A Modelling Tool

Coordinate methods are especially useful for deciding whether a relationship is linear and interpreting what a linear model means.
For data points $(n,C)$ (for example, number of units used $n$ and cost $C$), you can:
1. plot points and check if they lie close to a straight line,
2. compute gradients between pairs to see if the rate of change is roughly constant,
3. use a linear equation $C=mn+c$ as a model.
Interpretation is essential:
1. the gradient $m$ represents cost per unit (rate of change),
2. the y-intercept $c$ represents the fixed cost when $n=0$ (if $n=0$ is meaningful in context).

Case study

A "treasure map" is a fun way to see modelling in action: if each grid unit represents one league, then distance and midpoint calculations become real navigation decisions.
However, the model's validity depends on assumptions, for example whether the map scale is consistent and whether the terrain allows straight-line travel.

Rotations About The Origin Change Coordinates In Predictable Ways

Coordinate geometry also supports geometric transformations.
For rotations about the origin, there are simple coordinate rules.

Tip

Rotations about the origin:

For a point $P(a,b)$:

$90^\circ$ clockwise: $P'(b,-a)$
$90^\circ$ counterclockwise: $P'(-b,a)$
$180^\circ$: $P'(-a,-b)$

These rules are useful for quickly finding images of points without drawing every time.

Common Mistake

Be careful with the $180^\circ$ rule: both coordinates change sign, so $(a,b)$ becomes $(-a,-b)$.

Exam technique

Core toolkit of coordinate geometry:

Distance: $\sqrt{(x2-x1)^2+(y2-y1)^2}$
Midpoint: $\left(\tfrac{x1+x2}{2},\tfrac{y1+y2}{2}\right)$
Gradient: $\tfrac{y2-y1}{x2-x1}$
Parallel lines: same gradient
Perpendicular lines: gradients multiply to $-1$ (negative reciprocals)
Line equations: switch flexibly between $y=mx+c$, $y-y1=m(x-x1)$, and $ax+by+c=0$

Coordinate geometry (or analytic geometry) connects algebra and geometry by describing points and shapes using coordinates and equations.
It is a foundation for building and validating mathematical models, for example when mapping locations, designing layouts, or interpreting linear data.

Coordinates Describe Location Precisely

A point on a plane is located using an ordered pair $(x,y)$.

Definition

Cartesian coordinate plane

A grid formed by two perpendicular number lines, the x-axis (horizontal) and y-axis (vertical), used to locate points with ordered pairs $(x,y)$.

The x-coordinate tells you how far left or right to move from the origin.
The y-coordinate tells you how far down or up to move.
The origin is $(0,0)$.

Because every point has a unique coordinate pair, coordinate geometry lets you calculate geometric facts (like lengths and slopes) with algebra.

Distance Between Two Points Comes From Pythagoras

Suppose you have two points $A(x_1,y_1)$ and $B(x_2,y_2)$.
If you move from $A$ to $B$, the horizontal change is $\Delta x=x_2-x_1$ and the vertical change is $\Delta y=y_2-y_1$.
Using Pythagoras' theorem on the right triangle formed by these changes gives the distance formula.

Definition

Distance formula

For points $A(x_1,y_1)$ and $B(x_2,y_2)$, the distance between them is
$$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

Why Squaring Matters

The differences $x_2-x_1$ and $y_2-y_1$ can be negative, but distance cannot be negative.
Squaring removes sign, so the formula works no matter which point you subtract first.

Common Mistake

A very common error is to forget the squares and write $\sqrt{(x_2-x_1)+(y_2-y_1)}$.
The squares are essential because the distance is based on Pythagoras.

Example question

Find the distance between $(0,0)$ and $(5,12)$.

Solution

Here, $\Delta x=5-0=5$ and $\Delta y=12-0=12$.

$$AB=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$$

Exact Form Versus Decimal Form

Sometimes you are asked to leave answers as an exact surd, such as $\sqrt{n}$, and sometimes to round to a certain number of significant figures.

Tip

To keep an exact answer, simplify inside the square root only when there is a square factor.
For example, $\sqrt{72}=\sqrt{36\cdot 2}=6\sqrt{2}$

The Midpoint Is the Average of Coordinates

The midpoint of a line segment is the point exactly halfway between the endpoints.

Definition

Midpoint formula

For endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$, the midpoint is
$$M\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$

This works because moving halfway in the $x$ direction means averaging the $x$-coordinates, and similarly for $y$.

Example question

Find the midpoint of $A(1,4)$ and $B(4,8)$.

Solution

$$M\left(\frac{1+4}{2},\frac{4+8}{2}\right)=\left(\frac{5}{2},6\right)$$

A Useful Midpoint Property

If $M$ is the midpoint of $AB$, then $AM=\tfrac12 AB$.
One way to validate this is to:
1. compute $AB$ using the distance formula,
2. compute $AM$ using the distance formula,
3. show $AM=\tfrac12 AB$.
This kind of check is an example of using logic to validate a generalization.

Active recall

For $A(a,b)$ and $B(c,d)$:

Write down the midpoint $M$.
Use the distance formula to write expressions for $AB$ and $AM$.
What changes when you compare $(c-a)$ to $\left(\tfrac{c+a}{2}-a\right)$?

Gradient Measures Steepness And Direction

A straight line's gradient (also called slope) tells how steep it is and whether it rises or falls as you move left to right.

Definition

Gradient (slope)

For two distinct points $A(x_1,y_1)$ and $B(x_2,y_2)$ on a line, the gradient is
$$m=\frac{y_2-y_1}{x_2-x_1},\quad x_2\neq x_1$$

If $m>0$, the line rises left to right.
If $m<0$, the line falls left to right.
If $m=0$, the line is horizontal.
If $x_2=x_1$, the line is vertical and the gradient is undefined.

Common Mistake

Don't swap the order in the numerator and denominator inconsistently.
If you use $(y_2-y_1)$ then you must use $(x_2-x_1)$ with the same point order.

Example question

Find the gradient of the line through $A(0,0)$ and $B(1,4)$.

Solution

$$m=\frac{4-0}{1-0}=4$$

Parallel And Perpendicular Lines Have Predictable Gradients

Gradients let you recognize angle relationships between lines without measuring angles.

Definition

Parallel lines

Two non-vertical lines are parallel if they have the same gradient.

Definition

Perpendicular lines

Two non-vertical, non-horizontal lines are perpendicular if their gradients multiply to $-1$. If one line has gradient $m\,(m\neq 0)$, then a perpendicular line has gradient $-\frac{1}{m}$.

Note

Special Cases: Horizontal And Vertical

A horizontal line has gradient $0$ and a vertical line has undefined gradient, so the "negative reciprocal" rule cannot be applied directly in that form.

A horizontal line is perpendicular to a vertical line.
Horizontal lines are parallel to each other.
Vertical lines are parallel to each other.

Hint

When checking perpendicularity, first ask: "Is one line horizontal and the other vertical?"
If yes, they are perpendicular even though gradients do not multiply neatly.

Equations Of Straight Lines Can Be Written In Different Forms

A line can be represented by an equation in several equivalent forms.
Choosing an efficient form is part of good problem solving.

Slope-Intercept Form Highlights Gradient

Definition

Slope-intercept form

The equation of a non-vertical line can be written as $$y=mx+c$$ where $m$ is the gradient and $c$ is the $y$-intercept.

Hint

The y-intercept is where the line crosses the $y$-axis, at $(0,c)$.

Point-Slope Form Is Fast When You Know A Point And The Gradient

Definition

Point-slope form

A line through $(x_1,y_1)$ with gradient $m$ can be written as $$y-y_1=m(x-x_1)$$

Note

This is often the quickest way to build an equation from a point and a gradient.

Standard Form Is Useful For Intercepts And Some Exam Requirements

Definition

Standard form (linear)

A line can be written as $$ax+by+c=0$$ with constants $a,b,c$ (often integers, and sometimes with a required sign convention such as $a>0$).

Tip

To find intercepts quickly from standard form:

y-intercept: set $x=0$ and solve for $y$.
x-intercept: set $y=0$ and solve for $x$.

Example question

Find where the line $2y-3x-7=0$ intersects the axes.

Solution

On the $y$-axis, $x=0$: $$2y-7=0\Rightarrow y=\frac{7}{2}$$
So the y-intercept is $(0,\tfrac72)$
On the $x$-axis, $y=0$: $$-3x-7=0\Rightarrow x=-\frac{7}{3}$$
So the x-intercept is $(-\tfrac73,0)$

Exam technique

If an answer is required "in the form $ax+by+c=0$ with integers", avoid fractions by multiplying through by the lowest common multiple of denominators, then rearrange so one side is 0.

Finding A Line Equation In Common Situations

Through Two Points

Find the gradient $m=\dfrac{y2-y1}{x2-x1}$.
Use point-slope form with either point.
Convert to the required form (slope-intercept or standard).

Parallel To A Given Line

Parallel lines have the same gradient.
Use the given point to find the intercept.

Example question

The line $y=px+q$ is parallel to $y=2x-6$ and passes through $(-1,7)$. Find $p$ and $q$.

Solution

Parallel means $p=2$.
Substitute the point into $y=2x+q$: $$7=2(-1)+q=-2+q\Rightarrow q=9$$
So $p=2$ and $q=9$, and the line is $y=2x+9$

Perpendicular To A Given Line

Find the gradient of the given line.
Take the negative reciprocal to get the perpendicular gradient.
Use point-slope form.

Example question

Find the equation of the line through $S(3,7)$ perpendicular to $l_2: 3x+2y+2=0$, and give it in the form $ax+by+c=0$ with $a>0$.

Solution

First rewrite $l_2$ to see its gradient: $$3x+2y+2=0\Rightarrow 2y=-3x-2\Rightarrow y=-\frac{3}{2}x-1$$
So $m_2=-\tfrac32$
A perpendicular line has gradient $$m_1=-\frac{1}{m_2}=-\frac{1}{-\tfrac32}=\frac{2}{3}$$
Use point-slope form through $(3,7)$: $$y-7=\frac{2}{3}(x-3)$$
Expand: $$y-7=\frac{2}{3}x-2\Rightarrow y=\frac{2}{3}x+5$$
Convert to standard form with integers: $$3y=2x+15\Rightarrow 2x-3y+15=0$$

Coordinate Geometry As A Modelling Tool

Coordinate methods are especially useful for deciding whether a relationship is linear and interpreting what a linear model means.
For data points $(n,C)$ (for example, number of units used $n$ and cost $C$), you can:
1. plot points and check if they lie close to a straight line,
2. compute gradients between pairs to see if the rate of change is roughly constant,
3. use a linear equation $C=mn+c$ as a model.
Interpretation is essential:
1. the gradient $m$ represents cost per unit (rate of change),
2. the y-intercept $c$ represents the fixed cost when $n=0$ (if $n=0$ is meaningful in context).

Case study

A "treasure map" is a fun way to see modelling in action: if each grid unit represents one league, then distance and midpoint calculations become real navigation decisions.
However, the model's validity depends on assumptions, for example whether the map scale is consistent and whether the terrain allows straight-line travel.

Rotations About The Origin Change Coordinates In Predictable Ways

Coordinate geometry also supports geometric transformations.
For rotations about the origin, there are simple coordinate rules.

Tip

Rotations about the origin:

For a point $P(a,b)$:

$90^\circ$ clockwise: $P'(b,-a)$
$90^\circ$ counterclockwise: $P'(-b,a)$
$180^\circ$: $P'(-a,-b)$

These rules are useful for quickly finding images of points without drawing every time.

Common Mistake

Be careful with the $180^\circ$ rule: both coordinates change sign, so $(a,b)$ becomes $(-a,-b)$.

Exam technique

Core toolkit of coordinate geometry:

Distance: $\sqrt{(x2-x1)^2+(y2-y1)^2}$
Midpoint: $\left(\tfrac{x1+x2}{2},\tfrac{y1+y2}{2}\right)$
Gradient: $\tfrac{y2-y1}{x2-x1}$
Parallel lines: same gradient
Perpendicular lines: gradients multiply to $-1$ (negative reciprocals)
Line equations: switch flexibly between $y=mx+c$, $y-y1=m(x-x1)$, and $ax+by+c=0$

MYP Standard Mathematics Coordinate Geometry Basics Notes

MYP Standard Mathematics Coordinate Geometry Basics Notes

Coordinates Describe Location Precisely

Distance Between Two Points Comes From Pythagoras

Why Squaring Matters

Exact Form Versus Decimal Form

The Midpoint Is the Average of Coordinates

A Useful Midpoint Property

Gradient Measures Steepness And Direction

Parallel And Perpendicular Lines Have Predictable Gradients

Special Cases: Horizontal And Vertical

Equations Of Straight Lines Can Be Written In Different Forms

Slope-Intercept Form Highlights Gradient

Point-Slope Form Is Fast When You Know A Point And The Gradient

Standard Form Is Useful For Intercepts And Some Exam Requirements

Finding A Line Equation In Common Situations

Through Two Points

Parallel To A Given Line

Perpendicular To A Given Line

Coordinate Geometry As A Modelling Tool

Rotations About The Origin Change Coordinates In Predictable Ways

Coordinates Describe Location Precisely

Distance Between Two Points Comes From Pythagoras

Why Squaring Matters

Exact Form Versus Decimal Form

The Midpoint Is the Average of Coordinates

A Useful Midpoint Property

Gradient Measures Steepness And Direction

Parallel And Perpendicular Lines Have Predictable Gradients

Special Cases: Horizontal And Vertical

Equations Of Straight Lines Can Be Written In Different Forms

Slope-Intercept Form Highlights Gradient

Point-Slope Form Is Fast When You Know A Point And The Gradient

Standard Form Is Useful For Intercepts And Some Exam Requirements

Finding A Line Equation In Common Situations

Through Two Points

Parallel To A Given Line

Perpendicular To A Given Line

Coordinate Geometry As A Modelling Tool

Rotations About The Origin Change Coordinates In Predictable Ways

Number and Algebra Foundations

Coordinate Geometry and Linear Modelling

Functions and Quadratic Relationships

Sets, Logic and Probability

Geometry of Shapes, Surface Area and Volume

Statistical Measures and Data Representation

Right Triangles and Circle Geometry

Sequences, Formulae and Proportional Reasoning

Sampling Methods and Bivariate Data

MYP Standard Mathematics Coordinate Geometry Basics Notes

Number and Algebra Foundations

Coordinate Geometry and Linear Modelling

Functions and Quadratic Relationships

Sets, Logic and Probability

Geometry of Shapes, Surface Area and Volume

Statistical Measures and Data Representation

Right Triangles and Circle Geometry

Sequences, Formulae and Proportional Reasoning

Sampling Methods and Bivariate Data

MYP Standard Mathematics Coordinate Geometry Basics Notes

Coordinates Describe Location Precisely

Distance Between Two Points Comes From Pythagoras

Why Squaring Matters

Exact Form Versus Decimal Form

The Midpoint Is the Average of Coordinates

A Useful Midpoint Property

Gradient Measures Steepness And Direction

Parallel And Perpendicular Lines Have Predictable Gradients

Special Cases: Horizontal And Vertical

Equations Of Straight Lines Can Be Written In Different Forms

Slope-Intercept Form Highlights Gradient

Point-Slope Form Is Fast When You Know A Point And The Gradient

Standard Form Is Useful For Intercepts And Some Exam Requirements

Finding A Line Equation In Common Situations

Through Two Points

Parallel To A Given Line

Perpendicular To A Given Line

Coordinate Geometry As A Modelling Tool

Rotations About The Origin Change Coordinates In Predictable Ways

Coordinates Describe Location Precisely

Distance Between Two Points Comes From Pythagoras

Why Squaring Matters

Exact Form Versus Decimal Form

The Midpoint Is the Average of Coordinates

A Useful Midpoint Property

Gradient Measures Steepness And Direction

Parallel And Perpendicular Lines Have Predictable Gradients

Special Cases: Horizontal And Vertical

Equations Of Straight Lines Can Be Written In Different Forms

Slope-Intercept Form Highlights Gradient

Point-Slope Form Is Fast When You Know A Point And The Gradient

Standard Form Is Useful For Intercepts And Some Exam Requirements

Finding A Line Equation In Common Situations

Through Two Points

Parallel To A Given Line

Perpendicular To A Given Line

Coordinate Geometry As A Modelling Tool

Rotations About The Origin Change Coordinates In Predictable Ways