URGENT GEOMETRY PLEASE HELP

Question

The segment shown is half of AB^¯¯¯¯, where B(−5,1) is one endpoint of the segment and M(−3,3) is the midpoint of the segment.

What are the coordinates of point A?

Enter your answer as an ordered pair, formatted like this: (42, 53)

Answer 1

This is a right triangle. pts (α)-5,1 and (β)-3,3. side b=2; side a=2. Point (γ)=-2,1 (right angle). side c=2.828......... a^2+b^2=c^2.

Answer 2

The formula for the Midpoint is (x_m, y_m)=((x₁+x₂)/2 , (y₁+y₂)/2 ) where the subscript m stands for midpoint and (x₁,y₁) and (x₂,y₂) are the two endpoints. In this problem we are given one of the endpoints (-5,1) as well as the midpoint (-3,3).

The easiest way to solve this is to split the equation up so that we solve for x by itself and then y by itself.

So we get x_m=(x₁+x₂)/2. We plug in the x coordinate of the midpoint to get -3=(x₁+x₂)/2. Then we plug in the x coordinate of one of our endpoints to get -3=(-5+x₂)/2. If we multiply both sides by 2 we get -6=-5+x_2. Then we add five to both sides to get -1=x₂. So the x coordinate of our other endpoint is -1.

Now we repeat a similar process to solve for y. Our y coordinate of the midpoint is 3. So we have 3=(y₁+y₂)/2. Then we plug in the y coordinate for our original endpoint to get 3=(1+y₂)/2. We multiply both sides by 2 to get 6=1+y_2. Subtract 1 from both sides to get 5=y₂. So the y coordinate of our other endpoint is 5.

We put these two pieces of info together to show that our other endpoint is (-1,5).

The faster way to solve this problem is to think about it logically and this can be used to check your answer. If we started at an x coordinate of -5 and we know that at the midway point the x coordinate was -3 then that means we moved up +2 on the x axis. To go the other half of the distance we would add +2 again. This would take us from -3 to -1 on the x coordinate. This lines up with the way we solved it numerically.

Repeating the same process for y, we started at 1 and added +2 to get to our midpoint of 3. If we add two more that will take us to the other side of the midpoint and we will end up with 3+2=5. This also checks with how we solved the problem numerically