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.

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