EduNinja

[Maximum number: 4]

A is the point (1,5) and B is the point (3,9). M is the midpoint of AB.

Find the equation of the line that is perpendicular to AB and passes through M. Give your answer in the form y=m x+c.

y=

$y=-\frac{1}{2}x+8$
oe

Correct equivalent in different form scores 3.
M1 for gradient of $AB=\frac{9-5}{3-1}$ , $\frac{4}{2}$ , or 2
M1dep for gradient $p=-\frac{1}{\text{their grad of }AB}$
M1dep for substitution of their midpoint into $y=(\text{their }p)x+c$ oe, where their $p\ne0$

[Maximum number: 6]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

O is the origin (0,0), A is the point (8,1) and B is the point (2,5).

(a)

Find the equation of the perpendicular bisector of AB. Give your answer in the form y=m x+c.

y=

[ 4 ]

$y=\frac32x-\frac92$ oe
B1 for (5,3) oe
M1 for gradient $=-\frac1{\text{their gradient of }AB}$
M1 substituting their midpoint into y= their mx+c

(b)

The line AB meets the y-axis at P.

The perpendicular bisector of AB meets the y-axis at Q.
Find the length of PQ.

[ 2 ]

$\frac{65}{6}$ oe
M1 for their $\frac{19}{3}$ - their $-\frac92$ oe

[Maximum number: 3]

15 C is the point (5,-1) and D is the point (13,15).

Find the equation of the perpendicular bisector of CD. Give your answer in the form y=m x+c.

y=

$y=-\frac12x+\frac{23}{2}$

CAIE IGCSE Mathematics Extended E3.7 Perpendicular Lines Topic Practice

Question 1

Question 2

Question (a)

Question (b)

Question 3