Subjects geometry

Distance Parks 35894C

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1. **Problem:** Find the distance between points C(-2, 2) and D(4, -1) on a coordinate plane where each unit equals 25 miles. 2. **Formula:** Use the distance formula derived from the Pythagorean theorem: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate differences:** $$x_2 - x_1 = 4 - (-2) = 6$$ $$y_2 - y_1 = -1 - 2 = -3$$ 4. **Substitute into formula:** $$d = \sqrt{6^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}$$ 5. **Simplify:** $$\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \approx 6.708$$ 6. **Convert units:** Each unit is 25 miles, so distance in miles is: $$6.708 \times 25 = 167.7$$ 7. **Round:** The distance between the parks is approximately 168 miles.