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

Question

Which equation correctly relates p and q?

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

A. 

p + q = 7

B. 

-q − p = 7

C. 

p − q = 7

D. 

q − p = 7

Answer 1

slope of AB = (1-4)/(6-p) - =-3/(6-p)

slope of BC = (q-1)/(9-6) = (q-1)/3

since product of slopes for two perpendicular lines is -1:

-3 (q-1)

--- ------ = -1

(6-p) 3

-(q-1)

-------- = -1

(6-p)

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

q-1 = 6 - p

p + q = 7

Answer 2

Slope AB m_AB = (4 - 1)/(p - 6) = 3/(p - 6)

Slope BC m_BC = (q - 1)/(9 - 6) = (q - 1)/3

But because of orthogonality 3/(p - 6) · (q -1)/3 = - 1; 3(q - 1) = - 3p - 6); q - 1 = - p + 6; q + p = 7.

Answer is A. p + q = 7