How to solve distance problem

Question

Find the exact distance between the midpoint of the line segment from point
A to the x-axis and the midpoint of the line segment frompoint A to the y-axis given the point A to be (−5,−12). Be sure to simplify your solution completely. The answer can’t be a decimal or in decimal form. 

Answer 1

Reading this wordy problem carefully, I find M, first midpoint mentioned, to be (-5,-6) and N, 2nd midpoint mentioned, to be (-5/2,-12).

 

It helps to draw the figure plotting all these points in the third quadrant.  Now look at right triangle MAN.

 

Leg lengths are 6 and 5/2; use Pythagorean theorem to find hypotenuse distance MN, which I think is what is wanted.

 

Check everything carefully as you go.