Question

Show that the line joining the points (2,-3) and (-5, 1) is parallel to the line joining the points (7,-1) and (0, 3) and perpendicular to the line joining (4, 5) and (0,-2).

Answer 1

Let A (2,-3),B(-5, 1),C(7,-1), D (0, 3), E(4, 5), F(0,-2)

Line joining AB is parallel to the line joining CD, therefore slope of both the lines must be same

Slope of AB $=\frac{1-(-3)}{-5-2}=4/7$
Slope of CD $=\frac{3-(-1)}{0-7}=4/7$

Slope of both the lines are equal So, AB and CD lines are parallel

Slope of EF $=\frac{-2-\left(5\right)}{0-4}=7/4$

Slope of EF$\times$ Slope of CD = -4/7 $\times$ 7/4 = -1

Hence, EF is perpendicular to both the lines AB and CD.