Find the coordinates of the vertices of the triangle and compute the area of the triangle using the distance formula. (round to the nearest integer in units2)

We are asked to find two things, namely: 1. The coordinates of the vertices of the triangle.2. Compute the area of the triangle using the distance formula.Let's solve this exercise step by step, so:1. To do this we will see the the figure below to find out the points of each vertex. Thus, the three points are as follows:[tex]P_{1}(1, -5)[/tex][tex]P_{2}(4, -2)[/tex][tex]P_{3}(-3, 5)[/tex]2. The area of a triangle is given by this formula:[tex]A=\frac{bh}{2}[/tex]where b is the base and h the height of the triangle. We can use the Distance Formula to solve this problem so:[tex]b=\overline{P_{1}P_{2}}=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2} \\ \therefore b=\sqrt{(1-4)^2+[-5-(-2)]^2}=3\sqrt{2}[/tex][tex]h=\overline{P_{2}P_{3}}=\sqrt{(x_{2}-x_{3})^2+(y_{2}-y_{3})^2} \\ \therefore b=\sqrt{[4-(-3)]^2+(-2-5)^2}=3\sqrt{2}=7\sqrt{2}[/tex]Finally the area is:[tex]A=\frac{3\sqrt{2}\times 7\sqrt{2}}{2} \rightarrow \boxed{A=21 \ units^2}[/tex]