Question

Triangle ABC has coordinates A(-3, 4), B(3, 2), and C(1, -2). Find the area of triangle ABC.

Answer 1

Step 1: Write out the formula for finding the area of traingle given the three coordinates

`\begin{gathered} \text{say:} \\ A(x_1,y_1);B(x_2,y_2);C(x_3,y_3) \\ \text{Area}=(1)/(2)(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) \end{gathered}`

Step 2: Write out the given parameters

`\begin{gathered} A(-3,4);B(3,2);C(1,-2) \\ x_1=-3;y_1=4 \\ x_2=3;y_2=2 \\ x_3=1;y_3=-2 \end{gathered}`

Step 3: Substitute the parameters into the formula

`\begin{gathered} \text{Area}=(1)/(2)(-3(2--2)+3(-2-4)+1(4-2)) \\ =(1)/(2)(-3(4)+3(-6)+1(2)) \\ =(1)/(2)(-12-18+2) \\ =(1)/(2)(-28) \\ \text{Area}=\lvert-14\rvert \\ A=14 \end{gathered}`

Hence, the area is 14square unit