P,M and Q are three collinear points and PM=MQ.
If P is the point (-1,4) and M is the point (5,8), find the coordinates of the point Q.
What I've Done: I've found the distance MQ which is sqrt 52. I've made the equation $$\sqrt{52}=\sqrt{(5-x_1)^2 + (8-y_1)^2}$$
where $x_1$, $y_1$ are coordinates for $Q$. What do I do now? Help would be greatly appreciated.
Best Answer
This is easier to solve using the midpoint formula:
If $Q=(x,y)$, then you have $$\big(\frac{x+(-1)}{2},\frac{y+4}{2}\big)=(5,8);$$so now you can solve for x and y.
If you want to continue with your solution, though, find the equation for the line which passes through P and M, and then use this to solve for y in terms of x and then substitute into your formula.