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 (x_{1}, y_{1}) and (x_{2}, y_{2}) 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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