Question: 23. An artist determines the location of a mural on a wall by mapping out the mural on a coordinate plane. The mural forms a triangle with vertices located at $(-3, -5)$, $(-3, 7)$, and $(4, 7)$. What is the area of the triangle? A 84 square units B 42 square units C 38 square units D 19 square units
1. **State the problem:** We need to find the area of a triangle with vertices at $(-3, -5)$, $(-3, 7)$, and $(4, 7)$ on the coordinate plane.
2. **Formula for the area of a triangle on coordinate plane:**
The area $A$ of a triangle with base $b$ and height $h$ is given by:
$$A = \frac{1}{2} \times b \times h$$
3. **Identify the base and height:**
- The points $(-3, 7)$ and $(4, 7)$ lie on the same horizontal line $y=7$, so the segment between them is horizontal and can be the base.
- The length of the base $b$ is the distance between $x=-3$ and $x=4$:
$$b = 4 - (-3) = 4 + 3 = 7$$
- The height $h$ is the vertical distance from the third vertex $(-3, -5)$ to the base line $y=7$:
$$h = 7 - (-5) = 7 + 5 = 12$$
4. **Calculate the area:**
$$A = \frac{1}{2} \times 7 \times 12$$
5. **Simplify the multiplication:**
$$A = \frac{1}{2} \times 84$$
6. **Final calculation:**
$$A = 42$$
7. **Answer:** The area of the triangle is $42$ square units.
**Therefore, the correct choice is B 42 square units.