Question

Match each pair of points A and B to point C such that ∠ABC = 90°. A(3, 3) and B(12, 6) C(6, 52) A(-10, 5) and B(12, 16) C(16, -6) A(-8, 3) and B(12, 8) C(18, 4) A(12, -14) and B(-16, 21) C(-11, 25) A(-12, -19) and B(20, 45) A(30, 20) and B(-20, -15)

Answer 1

A(3, 3) and B(12, 6) = C(16, -6)

A(-10, 5) and B(12, 16) = C(18, 4)

A(-12, -19) and B(20, 45) = C(6, 52)

A(12, -14) and B(-16, 21) =C(-11, 25)

Explanation:

Answer 2

The correct option is;

A(-12, -19) and B(20, 45) matches with point C(6, 52) such that ∠ABC = 90°

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