CAIE IGCSE Additional Math 7.3 midpoint length and bisector problems

Use this coordinate-geometry topic to build perpendicular bisectors from midpoints and gradients, then apply distance conditions to coordinates.

Exam points

Find midpoints and lengths from coordinate pairs before forming line equations.
Use perpendicular gradients to construct bisectors in coordinate geometry problems.
Apply distance ratios or bisector conditions to solve for possible coordinates.

[Maximum number: 2]

Point A has coordinates (3,-1).
A circle has equation $(x-4)^{2}+(y+3)^{2}=5$ .

Given that AB is a diameter of the circle, find the coordinates of B.

$\binom{4}{-3}+\binom{1}{-2} \text { oe, soi }$

or using centre and point A e.g.
$\frac{3+x}{2}=4 \text { and } \frac{-1+y}{2}=-3$

or solve simultaneously the line y=-2 x+5 with the circle leading to 3 term quadratic $x^{2}-8 x+15[=0]$ with an attempt to solve

M1

Award M1 for the 2 equations

Award the M1 for the quadratic

(5,-5)

A1

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7.3. Solve midpoint, length and bisector problems question 1