How do I solve this problem?Help Please?

Question

Points S, T, and P lie on a number line. Their coordinates are 0,1, and x, respectively. Given SP=PT, what is the value of x?

This is for geometry and the section is called Use Midpoint and Distance formulas

Answer 1

x = 1/2

Answer 2

Since SP = PT,  P is the midpont between S and T.

Hence 0 and 1 are the endpoints and x is the midpoint.

(1+0)/2 = 1/2 = x

Answer 3

Allright.  Think of it this way:

If S is at 0, and T is at 1, then P (x) can be either to the left of S, in between S and T (between 0 and 1), or to the right of T (greater than 1).

Now if the distance from S to x is the same as the distance from T to x, then consider each case:

x to the left of S: the only way x could be here is if S and T were at the same point, otherwise the distance from each to x would be different, since S and T are at different points.

x to the right of S: Same as above, but reversed.

So x must be between S and T, right?

Now if you're between two points, what is the only place you can be if you are the same distance from each point?

Right.  You have to be right between the two points (the midpoint).

So since S is at 0, and T is at 1, the midpoint of 0 and 1 is 1/2.

Therefore, P (or x) must be at 1/2.