It's hard to understand what you are trying to say here. "by dividing the result by 2". Dividingwhatresult by 2?

I guess you mean to first use the Pythagorean formula to find the length of the line segment, then use the Pythagorean formula with an unknown point, equal to half the previous distance to get an equation for x and y. Yes, you can do that but it far harder than necessary.

Suppose and are the endpoints of the line segment. Then is the length of the line segment. Let (x, y) be the midpoint. Then we must have . In order to find the two coordinates, x and y, we need another equation. Okay, use the other endpoint: \sqrt{(x- x_0)^2+ (y- y_0)^2= \frac{1}{2}\sqrt{(x_1- x_0)^2+ (y_1- y_0)^2}[/tex].

If you square those two equations you get and

But it is far simpler to use "similar triangles" and get that the midpoint between and is .