Find the midpoint of a segment AB is (5, 3). What is the missing coordinates. A = (2, 5) and B = (8, y)Group of answer choicesy = 3y = -2y = 1y = 5
Question
Find the midpoint of a segment AB is (5, 3).
What is the missing coordinates.
A = (2, 5) and B = (8, y)
Group of answer choices
- y = 3
- y = -2
- y = 1
- y = 5
Solution
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula ((x1 + x2)/2, (y1 + y2)/2).
Given that the midpoint is (5, 3) and one of the endpoints is (2, 5), we can substitute these values into the formula to find the missing y-coordinate of the other endpoint.
So, we have:
(2 + x2)/2 = 5, which simplifies to x2 = 8. This matches the given x-coordinate of point B, so our substitution is correct.
(5 + y2)/2 = 3, which simplifies to y2 = 2*3 - 5 = 1.
So, the missing y-coordinate of point B is 1. Therefore, the correct answer is y = 1.
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