Question

The coordinates of A, B, and C in the diagram are A(p, 4), B(6, 1), and C(9, q). Which equation correctly relates p and q?

Answer 1

Refer to the diagram shown below.

Calculate the slope of line segment AB as m₁.

`m_(1) = (4-1)/(p-6)= (3)/(p-6)`

Calculate the slope of line segment BC as m₂.

`m_(2) = (q-1)/(9-6) = (q-1)/(3)`

The product of the slopes of perpendicular lines is equal to -1.
Therefore

`( (3)/(p-6))( (q-1)/(3))=-1 \\\\ (q-1)/(p-6)=-1 \\\\ q-1 = 6-q \\\\ p+q = 7`

The equation that relates p and q is p+q = 7

Answer: p + q = 7