Answer:
Answer is (C) ⇒ -7x - 5y = -48
Step-by-step 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)
