Question

triangle abc is a right triangle the length of bc is 5 units. the area of abc is square units. a(-9, 10) b(7, -2) c(4, -6)

Explanation:

Step1: Calculate length of AB

First, use the distance formula for points $A(-9,10)$ and $B(7,-2)$:
$$AB = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = \sqrt{(7-(-9))^2 + (-2-10)^2}$$
$$=\sqrt{(16)^2 + (-12)^2} = \sqrt{256 + 144} = \sqrt{400} = 20$$

Step2: Use right triangle area formula

Since $\triangle ABC$ is right-angled at $B$, area is $\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$, where $AB=20$ and $BC=5$.
$$\text{Area} = \frac{1}{2} \times AB \times BC = \frac{1}{2} \times 20 \times 5$$

Answer:

50 square units