If you know the coordinates of the midpoint and one endpoint, you can leverage the midpoint formula to reverse-engineer the location of the other endpoint. Applications in Real-World Scenarios.
Calculate Missing Endpoint With Midpoint Arithmetic
Assign the midpoint coordinates as \((M_x, M_y)\) and the known endpoint as \((x_1, y_1)\). This requires isolating \(x_2\) and \(y_2\) in the equation, resulting in the derived formulas \(x_2 = 2M_x - x_1\) and \(y_2 = 2M_y - y_1\).
Therefore, the missing endpoint is located at \((3, -1)\). Repeat this logic for the y-coordinate by doubling the y-midpoint and subtracting the y-value of the known point.
Calculate Missing Endpoint With Midpoint Arithmetic
For the y-coordinate, you calculate \(2(4) - 9\), which equals -1. Finding the missing endpoint of a line segment is a fundamental skill in coordinate geometry, essential for everything from basic graphing to advanced physics simulations.
More About How to find other endpoint with midpoint and endpoint
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