The point m(-6, -4) is translated 2 units right. what are the coordinates of the resulting point, m′?

The y coordinate stays the same 
just add 2 to the x coordinates gives

M(-4,-4)

If you plug the values for a, b, and c into the Pythagorean Theorem, you can get x alone to figure out the side lengths:

x² + 3x² - 1² = 3x² + 1²
Combine like terms
4x² - 1² = 3x² + 1²
Subtract 3x² from both sides
x² - 1² = 1²
Simplify 1²
x² - 1 = 1
Add 1 to both sides
x² = 2
Square root both sides
x = 1.41421

Then, simply plug in that number for x on each side! It comes out to a weird number, but I don't see any other way to solve it...
Hope this helps :)