Problem

The midpoint of \( \overline{\mathrm{AB}} \) is \( M(-4,0) \). If the coordinates of \( A \) are \( (-6,4) \), what are the coordinates of \( B \) ?

Answer

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Answer

Solve for \(x_B\) and \(y_B\): \(x_B = -2\) and \(y_B = -4\).

Steps

Step 1 ：Use the midpoint formula: \(M = \left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right)\).

Step 2 ：Substitute the given values: \(-4 = \frac{-6 + x_B}{2}\) and \(0 = \frac{4 + y_B}{2}\).

Step 3 ：Solve for \(x_B\) and \(y_B\): \(x_B = -2\) and \(y_B = -4\).

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