Answer: Choice B
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Explanation:
Let's say we had segment PQ. So the endpoints are P and Q. Let M be the midpoint of segment PQ.
Furthermore, let P have coordinates (x+6, y/3). Dividing by 3 is the same as multiplying by 1/3. So (1/3)y is the same as y/3.
Let Q have the coordinates (r,s). The goal is to express r and s in terms of x and y, as the answer choices indicate.
The midpoint M is located at (2,-5)
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For now, let's focus on the x coordinates of each point
- x coordinate of P is x+6
- x coordinate of Q is r
- x coordinate of M is 2
If we average the x coordinates of P and Q, we'll get the x coordinate of M
So we add up (x+6) and r, then divide by 2, and we should get 2 as a result
( (x coord of P) + (x coord of Q) )/2 = x coord of M
( (x+6) + (r) )/2 = 2
(x+6+r)/2 = 2
Let's solve for r
(x+6+r)/2 = 2
x+6+r = 2*2
x+6+r = 4
r = 4-x-6
r = -2-x
The x coordinate of point Q is -2-x
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We'll follow the same basic idea for the y coordinates
- The y coordinate of P is y/3
- The y coordinate of Q is s
- The y coordinate of M is -5
We then get
( (y coord of P) + (y coord of Q) )/2 = y coord of M
( (y/3) + (s) )/2 = -5
(y/3) + s = -5*2
(y/3) + s = -10
Now solve for s
(y/3) + s = -10
s = -10-(y/3)
This is the y coordinate of point Q.
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We found
- x coordinate of Q is -2-x
- y coordinate of Q is -10-(y/3)
Point Q is therefore located at (-2-x, -10-(y/3) )
This points to choice B as the final answer.
