Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A civil engineer is designing a new road. A section of the road needs to be represented on a coordinate plane as a line segment. If the midpoint of this segment is (3, 4) and one endpoint is (1, 6), what are the coordinates of the other endpoint?
- A(2, 5)
- B(5, 8)
- C(5, 2)
- D(4, 2)
Show answer & explanationAnswer & explanation
Correct answer: C. (5, 2)
The midpoint formula is ((x1 + x2)/2, (y1 + y2)/2). Let the known endpoint be (x1, y1) = (1, 6) and the midpoint be (xm, ym) = (3, 4). We need to find the other endpoint (x2, y2). For x: (1 + x2)/2 = 3 => 1 + x2 = 6 => x2 = 5. For y: (6 + y2)/2 = 4 => 6 + y2 = 8 => y2 = 2. So the other endpoint is (5, 2).
Why the other options are wrong
- A. This is the average of the x and y coordinates of the given endpoint and midpoint, not the other endpoint.
- B. Incorrect, the x-coordinate is correct, but the y-coordinate is incorrect.
- D. Incorrect, the x-coordinate is correct, but the y-coordinate is not.
Midpoint Formula (finding endpoint)
The midpoint formula states that the coordinates of the midpoint M of a line segment joining two points (x1, y1) and (x2, y2) are M = ((x1 + x2)/2, (y1 + y2)/2). This can be rearranged to find an unknown endpoint.
- The midpoint is exactly halfway between two endpoints.
- To find an unknown endpoint, double the midpoint coordinates and subtract the known endpoint coordinates.
- Applies in 2D and 3D coordinate systems.
Memory trick: Midpoint is 'Middle', Endpoints are 'Edges'.