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 ab is perpendicular to bc , the slope of ab x the slope of bc = -1.

this is a plato math question, will give 15 pts

attached is the diagram

answer choices:

a.
p − q = 7
b.
q − p = 7
c.
-q − p = 7
d.
p + q = 7

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  slope AB = (1 -4)/(6 -p) = 3/(p -6)

The slope of BC is ...

  slope BC = (q -1)/(9 -6) = (q -1)/3

The product of these is -1, so we have ...

  (slope AB)·(slope BC) = -1 = (3/(p -6))·((q -1)/3)

Multiplying by q -1 gives ...

  -(q -1) = p -6 . . . . . . the factors of 3 in numerator and denominator cancel

  1 = p + q -6 . . . . . . add q

  7 = p + q . . . . . . . . add 6 . . . . matches choice D

D. p + q = 7

Step-by-step explanation:

Just did this quiz on edmentum :P

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