Answer: (-1, 2)
Step-by-step explanation
Point A is located at the known point (-3,-6)
Point B is located at some unknown point (x,y)
Adding the x coordinates of each point, and dividing in half will get us the x coordinate of the midpoint (which is -2)
So,
(-3+x)/2 = -2
-3+x = -2*2
-3+x = -4
x = -4+3
x = -1
Therefore, the x coordinate of B is -1.
Follow similar steps to get the y coordinate of B.
(-6+y)/2 = -2
-6+y = -2*2
-6+y = -4
y = -4+6
y = 2
Therefore, point B is located at (-1, 2)
Use the midpoint formula on A(-3,-6) and B(-1,2) to see the midpoint is M(-2,-2). This will help confirm the answer.
Another way to confirm the answer is to use a graphing tool such as GeoGebra or Desmos. See the diagram below.