Question

Find k if PQ || RS and $P(2,4)Q(3,6),R(3,1),S(5,k)$

Answer 1

$PQ\parallel RS$

So, slope of line joining $P$ and $Q$ = slope of line joining $R$ and $S$

Slope $m$ of line joining the points $(x_1,y_1)$ and

$(x_2,y_2)$ is

$m=\frac{y_2-y_1}{x_2-x_1}$

So,

$m=\frac{6-4}{3-2}=\frac{k-1}{5-3}$

$\frac{k-1}{2}=2$

$k-1=4$

$k=5$