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36 votes
Can someone please help me? I don't understand how to solve this.

Can someone please help me? I don't understand how to solve this.-example-1
User Jeroen Vannevel
by
3.0k points

1 Answer

16 votes
16 votes

Answer:

(5, 15)

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

__

Solving these equations for x and y, you get ...

2Mx = x1 +x

x = 2Mx -x1

Similarly, ...

2My = y1 +y

y = 2My -y1

__

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).

_____

Additional comment

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.

User Martin Brugger
by
2.7k points
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