Question

A triangle on the coordinate plane has points located at A (2,5), B (5,9), and C (8,5). What is the area of the triangle? O A 10 square units O B. 24 square units O C 12 square units O D. 8 square units

Answer 1

`\begin{gathered} \text{The formula for area of the triangle is as follows}\colon \\ \text{Area}=(1)/(2)\lbrack x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\rbrack \\ \text{Here,} \\ x_1=2,y_1=5,x_2=5,y_2=9,x_3=8,y_3=5 \\ So,\text{ } \\ \text{Area}=(1)/(2)\lbrack2(9-5)+5(5-5)+8(5-9)\rbrack \\ \text{Area}=(1)/(2)\lbrack8+0-32\rbrack \\ \text{area}=12\text{ square unit.} \end{gathered}`