Subjects geometry

Distance Points 32Fedd

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1. **State the problem:** Find the distance between points $A(-2, -2)$ and $B(4, 6)$ 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 coordinates:** $$d = \sqrt{(4 - (-2))^2 + (6 - (-2))^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(4 + 2)^2 + (6 + 2)^2}$$ $$d = \sqrt{6^2 + 8^2}$$ 5. **Calculate the squares:** $$d = \sqrt{36 + 64}$$ 6. **Add the values inside the square root:** $$d = \sqrt{100}$$ 7. **Find the square root:** $$d = 10$$ 8. **Round to the nearest tenth:** The distance is already a whole number, so the distance between points A and B is $10.0$ units. **Final answer:** The distance between points A and B is **10.0** units.