Question

A B and B C form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of B C ? A. x + 3y = 16 B. 2x + y = 12 C. -7x − 5y = -48 D. 7x − 5y = 48

Answer 1

Answer is -7x - 5y = -48

Answer 2

Answer is (C) ⇒ -7x - 5y = -48

Explanation:

∵ AB ⊥ BC

∵ A (-3 , -1) , B (4 , 4)

Let C (x , y)

∵ (AC)² = (AB)² + (BC)²

∵ (AB)² = (4 - -3)² + (4 - -1)² = 49 + 25 = 74

∵ (BC)² = (x - 4)² + (y - 4)² = x² - 8x + 16 + y² - 8y + 16

∴ (BC)² = x² + y² - 8x - 8y + 32

∵ (AC)² = (x - -3)² + (y - -1)² = (x + 3)² + (y + 1)²

∴ (AC)² = x² + 6x + 9 + y² + 2y + 1 = x² + y² + 6x + 2y + 10

∴ x² + y² + 6x + 2y + 10 = 74 + x² + y² - 8x - 8y + 32

∴ 6x + 8x + 2y + 8y = 74 + 32 - 10

∴ 14x + 10y = 96 ⇒ ÷ 2

∴ 7x + 5y = 48 ⇒ × -1

∴ -7x - 5y = -48 ⇒ answer (C)