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) arrowBoth arrowBoth arrowBoth arrowBoth

i) A = (3, 3), B = (12, 6), C = (6, 52) : Not orthogonal, ii) A = (-10, 5), B = (12, 16), C = (6, 52) : Not orthogonal, iii) A = (-8, 3), B = (12, 8), C = (18, 4) : Not orthogonal, iv) A = (12, -14), B = (-16, 21), C = (-11, 25) : Orthogonal, v) A = (-12, -19), B = (20, 45) : Impossible orthogonality, vi) A = (30, 20), B = (-20, -15) : Impossible orthogonality.

Step-by-step explanation:

The statement indicates that segments AB and BC must be orthogonal. Vectorially speaking, this can be expressed by using the following expression from Linear Algebra:

Now, let is evaluate each choice:

i) A = (3, 3), B = (12, 6), C = (6, 52)

AB and BC are not orthogonal.

ii) A = (-10, 5), B = (12, 16), C = (6, 52)

AB and BC are not orthogonal.

iii) A = (-8, 3), B = (12, 8), C = (18, 4)

AB and BC are not orthogonal.

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

AB and BC are orthogonal.

v) A = (-12, -19), B = (20, 45)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

vi) A = (30, 20), B = (-20, -15)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

-50/3

step-by-step explanation: