Question

PLEASE PLEASE HELP AGAIN :( let P1 (-3, 4) and P2 (9, 10) be given points and suppose segment P1P2 is divided into 10 equal segments. determine the equation of a line perpendicular to P1P2 and passes through the point Q where W is a point on P1P2 six units from P2

i get how it's supposed to look like... but i'm having trouble finding Q
distance of p1 and p2 is 6sqrt5
slope of p1 and p2 is 1/2

tried doing midpoints and all but still no success :(

Answer 1

Well, let's see.
P1 (-3,4) P2 (9,10)

now, from the question, we know that Q is 4 units away from P1 and 6 units away from P2.
Therefore, x must have moved \[\frac{4}{10}*12=\frac{24}{5}\]
and y moved \[\frac{4}{10}*6=\frac{12}{5}\]
from P1.

So Q is \[( \frac{9}{5},\frac{32}{5})\]

Now that you know the slope, the rest won't be that hard.

Answer 2

Here is a picture

If you call the entire distance from p1 to p2 10
then you want to go 4/10 of the way. You know the x distance from p1 to p2 is 12
(9 - (-3))= 12
so set up a ratio to find how far to move in the x direction.
you can do the same to find the y value:

\[ \frac{y}{6}= \frac{4}{10} \]