Question: For the graph shown to the right, find (a) $AB$ to the nearest tenth and (b) the coordinates of the midpoint of $AB$.
(a) $AB = 8.9$ (Round to the nearest tenth as needed.)
(b) The coordinates of the midpoint of $AB$ are $(-1, -4)$. (Type an ordered pair.)
1. **State the problem:**
We are given points $A(-6, -2)$ and $B(4, -6)$ and need to find:
(a) The length of segment $AB$ rounded to the nearest tenth.
(b) The coordinates of the midpoint of $AB$.
2. **Formula for distance between two points:**
$$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
where $A = (x_1, y_1)$ and $B = (x_2, y_2)$.
3. **Calculate the distance $AB$:**
$$AB = \sqrt{(4 - (-6))^2 + (-6 - (-2))^2} = \sqrt{(4 + 6)^2 + (-6 + 2)^2} = \sqrt{10^2 + (-4)^2} = \sqrt{100 + 16} = \sqrt{116}$$
4. **Simplify and approximate:**
$$AB = \sqrt{116} \approx 10.7703$$
5. **Round to the nearest tenth:**
$$AB \approx 10.8$$
6. **Formula for midpoint:**
$$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$
7. **Calculate midpoint coordinates:**
$$M = \left( \frac{-6 + 4}{2}, \frac{-2 + (-6)}{2} \right) = \left( \frac{-2}{2}, \frac{-8}{2} \right) = (-1, -4)$$
**Final answers:**
(a) $AB \approx 10.8$
(b) Midpoint $M = (-1, -4)$