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?

Hint: Since is perpendicular to , the slope of × the slope of = -1.

Answer 1

`p + q= 7`

Step-by-step explanation

We determine the slope of each line using the slope formula;

`m = (y_2-y_1)/(x_2-x_1)`

The slope of BC is

`= ( q - 1)/(9 - 6)`

`( q - 1)/(3)`

The slope of AB is

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

`= - (3)/(6 - p)`

The two lines are perpendicular so the product of their slopes is -1.

`- (3)/(6 - p) * ( q - 1)/(3) = - 1`

This implies that,

`(q - 1)/(6 - p) = 1`

`q - 1=6 - p`

`q + p = 6 + 1`

`p + q= 7`

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