The midpoint of gh is m 5, 3. one endpoint is g 1, -5. find the coordinates of the other endpoint h.

Since m is the midpoint of gh, both of the x, y coordinates of m should be the average of that of g and h. Let h=(x,y). 5=(1+x)/2, x=2*5-1=9; 3=(-5+y)/2, y=2*3-(-5)=11. So h(9,11).

(9,11)

Explanation:
We are given that:
midpoint is (5,3)
one endpoint is (1,-5) that can be represented by (x1 , y1)
Assume that the coordinates of the other midpoint is (x2 , y2)
The x-coordinate of the midpoint is calculated using the following rule:
Xmidpoint = (x1+x2) / 2
5 = (1+x2) / 2
10 = 1 + x2
x2 = 10 - 1 = 9
The y-coordinate of the midpoint is calculated using the following rule:
Ymidpoint = (y1+y2) / 2
3 = (-5+y2) / 2
6 = -5+y2
y2 = 6+5 = 11
Based on the above calculations, the other endpoint is (9,11)

Hope this helps :)