IB Mathematics Applications & Interpretation Topic SL…

The line joining the points $A(2,-4)$ and $B(6,8)$ meets the $x$ - and $y$ -axes at the points $P$ and $Q$ , respectively.

Find the equation of line $AB$ and the length of the segment $PQ$ .

The line through the point $A(2,-3)$ is perpendicular to the line $2x + y = 5$ . This new line intersects the -axis at point and the -axis at point .

On a coordinate map, two emergency beacons are at $P(-5, 4)$ and $Q(1, -2)$ . The boundary separating their signal zones is the set of all points equidistant from and .

The triangle $ABC$ has vertices $A(-2,\,0)$ , $B (4, 0$ , and .

A phone operator has two masts, Mast Vest at $V(3,9)$ and Mast Ost at $O(18,9)$ . Grid distances are in kilometres. Assume all locations considered have coverage and a handset connects to the nearest mast. Each mast is a site, and its service region is its cell.

Find the equation of the line through $A$ and the coordinates of $P$ and $Q$ .

the ratio $PA : AQ$ .

the equation of this boundary, expressing your answer in the form $y = mx + c$ .

Find the equation of the perpendicular bisector of $[AB]$ .

Find the equation of the perpendicular bisector of $[AC]$ , giving your answer in the form $y=mx+c$ .

Find the coordinates of $P$ , the point of intersection of the two perpendicular bisectors.

Find the radius of the circle that passes through $A$ , $B$ , and $C$ .

Hence write down the equation of the circle passing through $A$ , $B$ , and $C$ .

Find the coordinates of the midpoint of $VO$ , and the gradient of $VO$ .

Write down the equation of the handover line between Mast Vest and Mast Ost.

why the relationship $m_1\times m_2=-1$ cannot be used to obtain the equation found in part (b).

The table below gives the position of the junction box of each of five streets, and the number of calls that box handles each day.

which mast serves each of the five streets, and the number of calls each day that each mast then carries.

A third mast, Mast Syd, is built at $S(18,\ 2)$ , due south of Mast Ost and with the same reach as the other two masts.

Find the equation of the line of points equidistant from Mast Ost and Mast Syd.

Show that the line of points equidistant from Mast Vest and Mast Syd has equation $15x-7y=119$ .

A sixth street, Fjordgata, has its junction box at $(14,\ 3)$ .

which of the three masts serves Fjordgata, using the distance from its junction box to each mast.

why the line found in part (b) is no longer the whole boundary between the areas served by Mast Vest and Mast Ost.

Havnegata	$6$	$14$	$340$
Fjellveien	$13$	$4$	$520$
Sandvik	$2$	$3$	$180$
Bruksgata	$16$	$11$	$610$
Lundevei	$9$	$12$	$260$

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank