Understanding the Midpoint Formula The foundation of this calculation is the midpoint formula, which states that the coordinates of the midpoint (M) between two points \((x_1, y_1)\) and \((x_2, y_2)\) are calculated as \(M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\). To find the x-coordinate of the missing endpoint, you calculate \(2(5) - 7\), which equals 3.
Find Missing Endpoint With Midpoint Formula Steps
Therefore, the missing endpoint is located at \((3, -1)\). To verify the accuracy of your work, you can average the endpoints \((7, 9)\) and \((3, -1)\); the average should return to your original midpoint \((5, 4)\), confirming the solution is correct.
The process involves identifying your known variables, plugging them into the derived equations, and performing the arithmetic carefully. Common Mistakes to Avoid Errors often occur when handling the signs of the numbers or the order of operations.
Find Missing Endpoint With Midpoint Formula Steps
Gather Your Known Values Begin by writing down the coordinates of the midpoint and the given endpoint. This requires isolating \(x_2\) and \(y_2\) in the equation, resulting in the derived formulas \(x_2 = 2M_x - x_1\) and \(y_2 = 2M_y - y_1\).
More About How to find other endpoint with midpoint and endpoint
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