difficult question

[momomath]

Point P lies on the line y=x. The coordinates of Q and T are (-1,8) and (8,1) respectively. The sum of the distances QP and TP is 18 units. Determine the coordinates of P.


I am having a hard time figuring this out. I would know how to solve this, if the the line QT was perpendicular to y=x, because then it would form a right triangle, but it doesn't. Do you know how to solve it?

 

[pka]

Point P lies on the line y=x. The coordinates of Q and T are (-1,8) and (8,1) respectively. The sum of the distances QP and TP is 18 units. Determine the coordinates of P.

Say that \(\displaystyle P: (a,a) \) because it is on \(\displaystyle y=x \).

Using the distance formula we get \(\displaystyle \sqrt{(a+1)^2+(a-8)^2}+\sqrt{(a-8)^2+(a-1)^2}=18 \).

Can you solve that?