Subjects geometry

Distance Points 7Aec5D

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1. **State the problem:** Find the distance between the points $ (16, -8) $ and $ (-11, -20) $ on the coordinate plane. 2. **Formula used:** The distance $ d $ between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is given by the distance formula: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ 3. **Substitute the given points:** $$ d = \sqrt{(-11 - 16)^2 + (-20 - (-8))^2} $$ 4. **Simplify inside the parentheses:** $$ d = \sqrt{(-27)^2 + (-12)^2} $$ 5. **Square the values:** $$ d = \sqrt{729 + 144} $$ 6. **Add the squares:** $$ d = \sqrt{873} $$ 7. **Calculate the square root and round to the nearest tenth:** $$ d \approx 29.5 $$ **Final answer:** The distance between the points is approximately $29.5$ units.