QuestionAugust 24, 2025

Find the distance between the points (-20,8) and (-16,-8) Also find the midpoint of the line segment joining the two points. The distance is square (Type an exact answer.using radicals as needed.) The midpoint is square (Type an ordered pair.)

Find the distance between the points (-20,8) and (-16,-8) Also find the midpoint of the line segment joining the two points. The distance is square (Type an exact answer.using radicals as needed.) The midpoint is square (Type an ordered pair.)
Find the distance between the points (-20,8) and (-16,-8) Also find the midpoint of the line segment joining the two points. The distance is square (Type an exact answer.using radicals as needed.) The midpoint is square (Type an ordered pair.)

Solution
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Answer

The distance is 4\sqrt{17} ### The midpoint is (-18, 0) Explanation 1. Calculate the distance Use the distance formula: **d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}**. Substitute x_1 = -20, y_1 = 8, x_2 = -16, y_2 = -8. d = \sqrt{(-16 + 20)^2 + (-8 - 8)^2} = \sqrt{4^2 + (-16)^2} = \sqrt{16 + 256} = \sqrt{272} = 4\sqrt{17}. 2. Calculate the midpoint Use the midpoint formula: **M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)**. Substitute x_1 = -20, y_1 = 8, x_2 = -16, y_2 = -8. M = \left(\frac{-20 + (-16)}{2}, \frac{8 + (-8)}{2}\right) = \left(\frac{-36}{2}, \frac{0}{2}\right) = (-18, 0).

Explanation

1. Calculate the distance<br /> Use the distance formula: **$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$**. Substitute $x_1 = -20$, $y_1 = 8$, $x_2 = -16$, $y_2 = -8$. <br /> $d = \sqrt{(-16 + 20)^2 + (-8 - 8)^2} = \sqrt{4^2 + (-16)^2} = \sqrt{16 + 256} = \sqrt{272} = 4\sqrt{17}$.<br /><br />2. Calculate the midpoint<br /> Use the midpoint formula: **$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$**. Substitute $x_1 = -20$, $y_1 = 8$, $x_2 = -16$, $y_2 = -8$.<br /> $M = \left(\frac{-20 + (-16)}{2}, \frac{8 + (-8)}{2}\right) = \left(\frac{-36}{2}, \frac{0}{2}\right) = (-18, 0)$.
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