QuestionAugust 11, 2025

7. The midpoint of overline (AB) is M(-3,-3) . If the coordinates of A are (2,1) , what are the coordinates of B? B(square ,square )

7. The midpoint of overline (AB) is M(-3,-3) . If the coordinates of A are (2,1) , what are the coordinates of B? B(square ,square )
7. The midpoint of overline (AB) is M(-3,-3) . If the coordinates of A are (2,1) , what are the coordinates of B? B(square ,square )

Solution
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Answer

B(-8, -7) Explanation 1. Use the midpoint formula The midpoint formula is M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right). Given M(-3, -3) and A(2, 1), let B(x, y) be the coordinates of point B. 2. Solve for x-coordinate of B Set up the equation for the x-coordinate: \frac{2 + x}{2} = -3. Solving gives x = -8. 3. Solve for y-coordinate of B Set up the equation for the y-coordinate: \frac{1 + y}{2} = -3. Solving gives y = -7.

Explanation

1. Use the midpoint formula<br /> The midpoint formula is $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Given $M(-3, -3)$ and $A(2, 1)$, let $B(x, y)$ be the coordinates of point B.<br />2. Solve for x-coordinate of B<br /> Set up the equation for the x-coordinate: $\frac{2 + x}{2} = -3$. Solving gives $x = -8$.<br />3. Solve for y-coordinate of B<br /> Set up the equation for the y-coordinate: $\frac{1 + y}{2} = -3$. Solving gives $y = -7$.
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