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.
Distance Points 32Fedd
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.