Question

What could be the value(s) of "x" if the distance between M(2,3) and N(x,15) is 13?

Answer 1

So you want to solve for the x-value given several key pieces of information.

If D(x, y) = √((x2 - x1)^2 + (y2 - y1)^2)
D(x, y) = 13
x1 = 2
y1 = 3
y2 = 15
Find x2.

Just use some simple algebra. In this instance, I'll just replace x2 with the variable X to make it easier to notate.

13 = √((X - 2)^2 + (15 - 3)^2)
13 = √((X - 2)^2 + 144)
169 = (X - 2)^2 + 144
25 = (X - 2)^2
(X - 2)^2 = 25
X - 2 = ±5
X = 7 OR X = -3

...BUT WAIT!

Go through it all again logically. What's wrong with one of these values? The problem: distances can't be negative! No one can travel a negative distance (unless you're talking about more intricate physics, but that's a whole different story), therefore the second answer is invalid. This leaves the proper answer to be X = 7.