how do I solve?

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.

Answer 1

draw a diagram

point A is (-5,-12)

assuming that the distances to the axes are perpendicular to the axes...

the midpoint of the segment from point A to the x-axis is (-5,-6)

the midpoint of the segment from point A to the y-axis is (-2.5,-12)

connect these points to form a right triangle

one leg is 6 units and the other leg is 2.5 units

the distance you want is the hypotenuse of this right triangle

d²=6²+(2.5)²

d²=36+6.25

d²=42.25

d=√42.25

d=6.5 units is the distance between the midpoints