Question

show by section formula that the points (3,-2),(5,2),(8,8) are coolinear

Answer 1

let (5,2) divide (3,-2) and (8,8) in k:1
$5 = \frac{3 \times1 + 8 \times k}{k + 1} \\ 5(k + 1) = 3 + 8k \\ 5k + 5 = 3 + 8k \\ 3k = 2 \\ k = \frac{2}{3} \\ y = \frac{ - 2 \times 1 + \frac{2}{3} \times 8 }{ \frac{2}{3} + 1 } \\ y = \frac{ - 6 + 16}{2 + 3} \\ y = \frac{10}{5} \\ y = 2 \\ y \: coordinate \: satisfies \: value \: of \: k \\ hence \: these \: points \:are \: colinear$