ANSWER
[tex]p + q= 7[/tex]
EXPLANATION
We determine the slope of each line using the slope formula;
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
The slope of BC is
[tex] = \frac{ q - 1}{9 - 6} [/tex]
[tex] \frac{ q - 1}{3} [/tex]
The slope of AB is
[tex] = \frac{1 - 4}{6 - p} [/tex]
[tex] = - \frac{3}{6 - p} [/tex]
The two lines are perpendicular so the product of their slopes is -1.
[tex] - \frac{3}{6 - p} \times \frac{ q - 1}{3} = - 1[/tex]
This implies that,
[tex]\frac{q - 1}{6 - p} = 1[/tex]
[tex]q - 1=6 - p[/tex]
[tex]q + p = 6 + 1[/tex]
[tex]p + q= 7[/tex]
.
