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? ↔

Question

3 years ago

11

↔ ↔ ↔ Hint: Since AB is perpendicular to BC, the slope of AB × the slope o BC = -1. A. -q − p = 7 B. q − p = 7 C. p − q = 7 D. p + q = 7

1 answer:

aivan3 [116] · Answer 1 · 2022-07-31T08:48:27+03:00

Answer:

D. p + q = 7

Step-by-step explanation:

The slope of AB is ...

mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)

The slope of BC is ...

mBC = (q -1)/(9 -6) = (q -1)/3

We want the product of these slopes to be -1:

mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)

-(q-1)/(6 -p) = -1 . . . . cancel factors of 3

q -1 = 6 -p . . . . . multiply by -(6 -p)

q + p = 7 . . . . . matches choice D