Question

what is the area of this triangle?
a. $a=\frac{1}{2}(y_3 - y_2)(x_3 - x_1)$
b. $a=\frac{1}{2}(y_3 - y_1)(x_3 - x_1)$
c. $a=\frac{1}{2}(y_3 - y_1)(x_2 - x_1)$
d. $a=\frac{1}{2}(y_2 - y_1)(x_3 - x_1)$
e. $a=\frac{1}{2}(y_2 - y_1)(x_2 - x_1)$

Explanation:

Step1: Identify base length

The base is the horizontal distance between $(x_1,y_1)$ and $(x_3,y_3)$, so base $= x_3 - x_1$.

Step2: Identify height length

The height is the vertical distance between $(x_1,y_1)$ and $(x_1,y_2)$, so height $= y_2 - y_1$.

Step3: Apply triangle area formula

Area $A = \frac{1}{2} \times \text{base} \times \text{height}$
Substitute base and height: $A = \frac{1}{2} (y_2 - y_1) (x_3 - x_1)$

Answer:

D. $A = \frac{1}{2} (y_2 - y_1) (x_3 - x_1)$