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?

Answer 1

nice

Answer 2

@imqwerty can you help with this

Answer 3

sure dude :)
but where the diagram? :o

Answer 4

pls post the diagram which is given with the question :)

Answer 5

oh sorry give me a moment

Answer 6

alright

Answer 7

AB and BC are perpendicular to each other
and the product of slopes of perpendicular lines is equal to \(\color{orangered}{-1}\)

so 1st we find out the slopes of AB and BC
we will use this info to find the slope-
the slope of a line passing through 2 points say \((x_1,y_1)\) and \((x_2,y_2)\) is given like this-
\(slope=\large \frac{y_2-y_1}{x_2-x_1}\)

slope of AB-
it passes through A(p, 4) and B(6, 1)
slope of AB= \(\large \frac{1-4}{6-p}=\frac{-3}{6-p}\)

slope of BC-
it passes through B(6, 1) and C(9, q)
slope of BC= \(\large \frac{q-1}{9-6}=\frac{q-1}{3}\)

the product of slopes of AB and BC must be -1

so

\(\Large \frac{-3}{6-p} \times \frac{q-1}{3}=-1\)

simplify from here and then you will get the relation between p and q :)

the relation is nothing but an expression containing p and q both in it

Answer 8

ok ty that was a lot of help man