Q. 115.0( 1 Vote )

The line joining the points A (0, 5) and B (4, 2) is perpendicular to the line joining the points C (1, 2) and D (5, b). Find the value of b.

Answer :

Line joining points A (0, 5) and B (4, 2) IA parallel to the line joining the points C (–1, –2) and D (5, b)


The two lines are perpendicular only if the multiplication of their slope is equal to 1.


(Slope of AB) × (Slope of CD) = 1


Slope of line passing through (x1, y1) and (x2, y2) is



Slope of AB is:


A (0, 5) and B (4, 2)




Slope of CD is:


C (–1, –2) and D (5, b)




The two lines are perpendicular only if the multiplication of their slope is equal to 1.


(Slope of AB) × (Slope of CD) = –1





–b – 2 = –1 × 8


–b – 2 = –8


–b = –8 + 2


– b = – 6


b = 6


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