QuestionAugust 26, 2025

3.Find the coordinates of the missing endpoint if B is the midpoint of overline (AC) C(-10,22) B(-8,17)

3.Find the coordinates of the missing endpoint if B is the midpoint of overline (AC) C(-10,22) B(-8,17)
3.Find the coordinates of the missing endpoint if B is the midpoint of overline (AC) C(-10,22) B(-8,17)

Solution
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Answer

A(-6, 12) Explanation 1. Use Midpoint Formula The midpoint formula is B = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right). Given B(-8,17) and C(-10,22), let A(x_1, y_1) be the missing endpoint. 2. Set Up Equations For the x-coordinate: -8 = \frac{x_1 - 10}{2}; for the y-coordinate: 17 = \frac{y_1 + 22}{2}. 3. Solve for x_1 Multiply both sides of -8 = \frac{x_1 - 10}{2} by 2: -16 = x_1 - 10. Solve: x_1 = -6. 4. Solve for y_1 Multiply both sides of 17 = \frac{y_1 + 22}{2} by 2: 34 = y_1 + 22. Solve: y_1 = 12.

Explanation

1. Use Midpoint Formula<br /> The midpoint formula is $B = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Given $B(-8,17)$ and $C(-10,22)$, let $A(x_1, y_1)$ be the missing endpoint.<br />2. Set Up Equations<br /> For the x-coordinate: $-8 = \frac{x_1 - 10}{2}$; for the y-coordinate: $17 = \frac{y_1 + 22}{2}$.<br />3. Solve for $x_1$<br /> Multiply both sides of $-8 = \frac{x_1 - 10}{2}$ by 2: $-16 = x_1 - 10$. Solve: $x_1 = -6$.<br />4. Solve for $y_1$<br /> Multiply both sides of $17 = \frac{y_1 + 22}{2}$ by 2: $34 = y_1 + 22$. Solve: $y_1 = 12$.
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