Problem

Given a line segment with start point A(2,3) and midpoint M(5,7), find the coordinates of the end point B.

Answer

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Answer

Step 3: Solving for \(x_B\) and \(y_B\), we get \(x_B = 2*5 - 2 = 8\) and \(y_B = 2*7 - 3 = 11\).

Steps

Step 1 ：Step 1: The coordinates of the midpoint M of a line segment AB with endpoints A and B are given by the formula \(M = \left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right)\).

Step 2 ：Step 2: Substituting the given values into the formula, we get \((5, 7) = \left(\frac{2 + x_B}{2}, \frac{3 + y_B}{2}\right)\).

Step 3 ：Step 3: Solving for \(x_B\) and \(y_B\), we get \(x_B = 2*5 - 2 = 8\) and \(y_B = 2*7 - 3 = 11\).

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