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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?

The coordinates of A B and C in the diagram are Ap 4 B6 1 and C9 q Which equation correctly relates p and q class=

Respuesta :

Refer to the diagram shown below.

Calculate the slope of line segment AB as m₁.
[tex]m_{1} = \frac{4-1}{p-6}= \frac{3}{p-6} [/tex]

Calculate the slope of line segment BC as m₂.
[tex]m_{2} = \frac{q-1}{9-6} = \frac{q-1}{3} [/tex]

The product of the slopes of perpendicular lines is equal to -1.
Therefore
[tex]( \frac{3}{p-6})( \frac{q-1}{3})=-1 \\\\ \frac{q-1}{p-6}=-1 \\\\ q-1 = 6-q \\\\ p+q = 7 [/tex]

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

Answer:  p + q = 7
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