Geometry CBE Practice Exam

What are the coordinates of the midpoint of segment AB with A(1,3) and B(5,7)?

(2,5) (3,5) (3,4) (4,5)

Correct Answer:

(3,5)

Explanation:

The midpoint of a segment in the coordinate plane is found by averaging the x-coordinates and the y-coordinates of the endpoints. For A(1,3) and B(5,7), the x-coordinates average to (1+5)/2 = 3, and the y-coordinates average to (3+7)/2 = 5. So the midpoint is (3,5). You can also see this by noting that x increases by 4 and y increases by 4 from A to B, so halfway along adds 2 to each coordinate: (1+2, 3+2) = (3,5).

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