Question

If points A(4,5), B(1,1) and C (-2,5) are vertices of an isosceles triangle, determine area (in sq. units) of triangle ABC (use the formula of area of triangle by coordinates)

Answer 1

Formula of area of triangle by coordinates is:

`\text{area}=(1)/(2)\lvert x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\rvert`
`\begin{gathered} x_1=4 \\ x_2=1 \\ x_3=-2 \\ y_1=5 \\ y_2=1 \\ y_3=5 \end{gathered}`

area is:

`\begin{gathered} \text{Area}=(1)/(2)\lvert4(1-5)+1(5-5)-2(5-1)\rvert \\ =(1)/(2)\lvert-16+0-8\rvert \\ =(24)/(2) \\ =12 \end{gathered}`

Area of triangle is 12 sq. unit