Maths / Coordinate Geometry / Section Formula

QUESTION

Determine the ratio in which the point P(m,6) divides the join of A(-4,3) and B (2,8) Also find the value of m.

EXPLANATION
Explain TypeExplanation Content
Text

A(-4,3), B(2,8) and P(m,6)

Let P divides the join of AB in the ratio of k : 1

$\therefore$ y coordinate of p = $\frac{k\times 8+1\times 3}{k+1}\\ \Rightarrow 6=\frac{8k+3}{k+1}\Rightarrow 6k+6=8k+3\Rightarrow 2k=3 \Rightarrow k=3/2$

$\therefore$divides the join of AB in the ratio of 3:2

x coordinate of p = $\frac{3\times 2+2\times d (-4)}{3+2}$

$\Rightarrow m=\frac{6-8}{5}\Rightarrow m=-2/5$

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