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.
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Prove that the line through (– 2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).
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Let the slope of the line through points (– 2, 6) and (4, 8) be m1
So, m1 = (y2 – y1)/ (x2 – x1)
= (8 – 6)/ (4 + 2)
= 2/6
= 1/3
And, let the slope of the line through (8, 12) and (4, 24) be m2
So, m2 = (y2 – y1)/ (x2 – x1)
= (24 – 12)/ (4 – 8)
= 12/ (-4)
= -3
Now, product of slopes is
m1 x m2 = 1/3 x (-3) = -1
Thus, the lines are perpendicular to each other.