How to solve for the values of these variables?

[trexyfrost]

I'm having a rough time solving this coordinate geometry problem: "The equation of the line that contains the perpendicular bisector of the segment that joins the points R(-8, t) and S(2, -3) is 2y + 5x = k. Find the values of k and t."

This book's author only gives me the answers (k = -25, t = -7), but I'm trying to figure out HOW to solve this problem. I've tried converting the equation for the perpendicular bisector line into slope-intercept form (y=(-5x+k)/2) so I can extract the negative reciprocal of its slope to formulate the equation for line RS, but I'm not sure how to proceed with that when the slope, x-coordinate, and y-intercept are divided by two....does k even equal the y-intercept? Please teach me, thank you.

 

[Dr.Peterson]

I hope you recognize that your equation y=(-5x+k)/2 can be written as y=(-5/2)x + (k/2), so that we can read off the slope as -5/2 and the y-intercept as k/2.

If that isn't your issue, please show your work so we can see where you are having trouble.

 

[lev888]

I hope you recognize that your equation y=(-5x+k)/2 can be written as y=(-5/2)x + (k/2), so that we can read off the slope as -5/2 and the y-intercept as k/2.

If that isn't your issue, please show your work so we can see where you are having trouble.

I was trying to get the OP to work this out on the other forum, I guess he/she decided to take a shortcut

 

[Dr.Peterson]

I assumed that anyone who has gone far enough to be given this relatively complex problem couldn't possibly not yet know how to find the slope when there is a division involved. Sometimes I'm amazed.