Question

A, B, C, and D are four points on the same straight line, and AB = BC = CD. If A is (-2, 15), C is (4, a), and D is (b, 3), then (a, b) is:

[1 mark]

Answer 1

C divides A and D in the ratio of 2:1.

By the section formula,

$P(x,y)=\left(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n}\right)$

$(4,a)=\left(\frac{2\left(b\right)+1(-2)}{3},\frac{2\left(3\right)+1\left(15\right)}{3}\right)$

$12=2b-2$

$a=\frac{21}{3}=7$

$(a,b)=(7,7)$