Question

Find the equation of the diagonals of quadrilateral whose vertices are $(1,2),(-2,-1),(3,6)$ and $(6,8)$.

Answer 1

$A(-2,-1)$

$B(3,6)$

$C(6,8)$

$D(1,2)$

Diagonal $AC$

$y+1=\frac{8+1}{6+2}(x+2)$

$y+1=\frac{9}{8}(x+2)$

$\Rightarrow 8y=9x+10$ ……...$AC$

Diagonal $BD,$

$y-2=\frac{6-2}{3-1}(x-1)$

$\Rightarrow y-2=2(x-1)$

$\Rightarrow y=2x$ ……….$BD.$