Math
posted by Aldwin on .
The coordinates of the endpoints of a line segment PQ are P(3,7) and Q(11,6). Find the coordinates of the point R on the yaxis such that PR = QR.
Please include the workings, as I would like to be able to perform these problems unassisted in the future (I just have trouble remembering the formulas).
Thank you anyone who answers this question :D

A point on the yaxis has coordinates (0,y).
The distance from (0,y) to P(3,7) is the diagonal of a rectangle which has sides (30) and (7y)
similarly for Q: the distances are (110) and (6y)
So,
PR = √(3^2 + (7y)^2)
QR = √(11^2 + (6y)^2)
to have PR=QR, you need
√(3^2 + (7y)^2) = √(11^2 + (6y)^2)
square both sides to get rid of the radicals:
9+(7y)^2 = 121+(6+y)^2
9+4914y+y^2 = 121+36+12y+y^2
collect terms (the y^2's go away  yay!)
26y = 99
y = 99/26
so, the point is (0,99/26)
odd answer, but hey, 99/26 is just a number, like 3 or 5. 
oops,
26y = 99, so
y = 99/26