if your given the midpoint= o,-3 and point A= 0,5 algebraically how do you find the other point?

Given the midpoint M(0,-3) . One end point is A(0,5). To find the other end point.

Solution:

Given the end points whose coordinates are (x1,y1) and (x2,y2), the mid point is given by ( x1+x2)/2 , (y1+y2)/2. We use this idea when mid point  and one end point is known is known.

So M(0,-3 ) = ((x1+x2)/2 , (y1+y2)/2)...(1)  Given ( x1, y1) = A(0,5) . To determine (x2,y2). So substituting x1= 0 and y1 = 5 in eq(1), we get:

M(0,3) = ((0+x2)/2 , (5+y2)). Now equate x coordinates on both sides  and also do so for y coordinates on both sides:

0 =(0+x2)/2 . Or x2 = 0

-3 =( 5+y2)/2. Or 5+y2 = -6. So y2 = -6-5 = -11.

So (x2,y2) = (0,-11).