Question

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)

Answer 1

21 units

Explanation:

Answer 2

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:
`P_(1)(1, -5)`
`P_(2)(4, -2)`

`P_(3)(-3, 5)`

2. The area of a triangle is given by this formula:

`A=(bh)/(2)`

where b is the base and h the height of the triangle. We can use the Distance Formula to solve this problem so:

`b=\overline{P_(1)P_(2)}=\sqrt{(x_(1)-x_(2))^2+(y_(1)-y_(2))^2} \\ \therefore b=√((1-4)^2+[-5-(-2)]^2)=3√(2)`

`h=\overline{P_(2)P_(3)}=\sqrt{(x_(2)-x_(3))^2+(y_(2)-y_(3))^2} \\ \therefore b=√([4-(-3)]^2+(-2-5)^2)=3√(2)=7√(2)`

Finally the area is:

`A=(3√(2)* 7√(2))/(2) \rightarrow \boxed{A=21 \ units^2}`