Given:
The vertices of the triangle are (-3,-3), (-3,2), and (1,2).
Required:
We need to find the area of the given triangle.
Explanation:
Mark the points on the graph and join them.
A(-3,2), B(-3,-3), and C(1,2).
The given triangle is a right-angled triangle.
The height of the given triangle is the length of AB.
The base length of the given triangle is the length of AC.
Consider the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Use the distance formula to find the length of the line segments.
Consider the points A(-3,2) and B(-3,-3),
[tex]Substitute\text{ }x_1=-3,y_1=2,x_2=-3\text{ and }y_2=-3\text{ in the formula.}[/tex][tex]AB=\sqrt{(-3-(-3))^2+(-3-2)^2}[/tex][tex]AB=\sqrt{(0)^2+(-5)^2}[/tex][tex]AB=5units[/tex]Consider the points A(-3,2) and C(1,2).
[tex]Substitute\text{ }x_1=-3,y_1=2,x_2=1\text{ and }y_2=2\text{ in the formula.}[/tex][tex]AC=\sqrt{(1-(-3))^2+(2-2)^2}[/tex][tex]AC=\sqrt{(4)^2+(0)^2}[/tex][tex]AC=4[/tex]We get h=AB=5 and b=AC=4.
Consider the area of the triangle formula.
[tex]A=\frac{hb}{2}[/tex]Substitute h=5 and b=4 in the formula.
[tex]A=\frac{5\times4}{2}[/tex][tex]A=10units^2[/tex]Final answer:
[tex]A=10units^2[/tex]