Answer:
The correct option is;
A(-12, -19) and B(20, 45) matches with point C(6, 52) such that ∠ABC = 90°
Step-by-step explanation:
Given slope AB =
A point is perpendicular to two points
Where A(3, 3), B(12, 6) C(6, 52) we have;
Slope AB = (3 - 6)/(3 - 12) = -3/(-9) = 1/3
Slope BC = -3
y - 12 = -3(x - 6)
y = -3x + 18 + 12 = -3x + 30
A(-10, 5) and B(12, 16)
Slope AB = (5 - 16)/(-10 - 12) = -11/(-22) = -1/2
Slope BC = 2
y - 16 = 2(x - 12)
y = 2x - 24 + 16 = 2x - 8
A(-8, 3) and B(12, 8)
Slope AB = (3 - 8)/(-8 - 12) = -5/(-20) = -1/4
Slope BC = -4
y - 8 = -4(x - 12)
y = -4x + 48 + 8 = -4x + 56
A(12, -14) and B(-16, 21)
Slope AB = (-14 - 21)/(12 + 16) = -35/(28)
Slope BC = 28/35
y - 21 = 28/35(x + 16)
y = 28/35x + 28/35*16 + 21 = -4x + 56
A(-12, -19) and B(20, 45)
Slope AB = (-19 - 45)/(-12 - 20) = 2
Slope BC = -1/2
y - 45 = -1/2(x - 20)
y = -1/2x + 10 + 45 = -1/2x + 55
Which corresponds with the point C(6, 52)
A(30, 20) and B(-20, -15)
Slope AB = (20 + 15)/(30 + 20) = 35/50 = 7/10
Slope BC = -10/7
y + 15 = -10/7(x + 20)
y = -10/7x - 10/7*20 - 15 = -10/7x - 305/7
