ICSE Board Question Based on Equation of a Straight Line Chapter of M.L Aggarwal for class10

In this question You have to Prove that the line through two given co-ordinates is perpendicular to the line through another two co-ordinates.

This is the Question Number 25, Exercise 12.2 of M.L Aggarwal.

Deepak BoraNewbie

# Prove that the line through (– 2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).

Share

Let the slope of the line through points (– 2, 6) and (4, 8) be m

_{1}So, m

_{1}= (y_{2}– y_{1})/ (x_{2}– x_{1})= (8 – 6)/ (4 + 2)

= 2/6

= 1/3

And, let the slope of the line through (8, 12) and (4, 24) be m

_{2}So, m

_{2}= (y_{2}– y_{1})/ (x_{2}– x_{1})= (24 – 12)/ (4 – 8)

= 12/ (-4)

= -3

Now, product of slopes is

m

_{1}x m_{2}= 1/3 x (-3) = -1Thus, the lines are perpendicular to each other.