Answer:
(5, 15)
Step-by-step explanation:
The problem statement tells you how to solve it. You are expected to know what the midpoint formula is.
You are given that (x, y) is the unknown end point. If (Mx, My) is the midpoint, and (x1, y1) is one end point, the midpoint formula tells you ...
Mx = (x1 +x)/2
My = (y1 +y)/2
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Solving these equations for x and y, you get ...
2Mx = x1 +x
x = 2Mx -x1
Similarly, ...
2My = y1 +y
y = 2My -y1
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Filling in the given coordinates, this becomes ...
x = 2(-2) -(-9) = -4 +9 = 5
y = 2(7) -(-1) = 14 +1 = 15
The other endpoint is (5, 15).
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<em>Additional comment</em>
I like to write the midpoint formula for points A and B as ...
M = (A +B)/2
where A and B each represent an ordered pair (or triple, in 3 dimensions). The arithmetic is done element-by-element on the ordered pairs, so this formula is equivalent to the one above.
If you solve it for B, you get ...
B = 2M - A . . . . the other endpoint given the midpoint and one endpoint
This might be a formula you want to add to your list of useful formulas in Algebra.
