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.

The coordinates of A, B, and C are in the diagram. AB and BC intersect at point B are 90 degrees.
A.
q − p = 7
B.
p − q = 7
C.
p + q = 7
D.
-q − p = 7

Answer 1

C. 3 + 4 = 7 YES

Explanation:

It is difficult to image the diagram, but see the attached graph and check for accuracy. The three points were added:

A (p,4),

B (6,1), and

C (9,q)

The unknowns p was given a value of 3 so that the line AB has a negative slope of -1. Line BC is said to intersect at point B at 90 degrees. A perpendicular line will have a slope that is the negative inverse of the first line. In this case, the slope would be 1.

This line goes through point C at x = 9. The y value would therefore need to be 4, so Point C becomes (9,4).

Line AB is equation y = -1x + 7.

Line BC is equation y = x - 5

p = 3, so point A is (3.4)

q = 4, so point C is (9,4)

=

A. q − p = 7 A. 4 − 3 = 7 NO

B. p − q = 7 B. 3 − 4 = 7 NO

C. p + q = 7 C. 3 + 4 = 7 YES

D. -q − p = 7 D. -4 − 3 = 7 NO