Question

Find the perimeter of the following triangle.

Answer 1

Hello!

To find the perimeter of the triangle, we need to find the length of all the sides using the distance formula.

The distance formula is:
`d =√((x_2-x_1)^2+(y_2-y_1)^2)`.

First, we can find the distance between the points (-3, -1) and (2, -1). The point (-3, -1) can be assigned to
`(x_(1),y_(1))`, and (2, -1) is assigned to
`(x_(2),y_(2))`. Then, substitute the values into the formula.

`d =\sqrt{(2 - (-3))^(2)+ (-1 - (-1))^(2)}`

`d =\sqrt{5^(2)+0^(2)}`

`d =√(25) = 5`

The distance between the points (-3, -1) and (2, -1) is 5 units.

Secondly, we need to find the distance between the points (2, 3) and (2, -1). Assign those points to
`(x_(1),y_(1))` and
`(x_(2),y_(2))`, then substitute it into the formula.

`d =\sqrt{(2 - 2)^(2)+ (-1 - 3)^(2)}`

`d =\sqrt{0^(2)+(-4)^(2)}`

`d =√(16) = 4`

The distance between the two points (2, 3) and (2, -1) is 4 units.

Finally, we use the distance formula again to find the distance between the points (-3, -1) and (2, 3). Remember the assign the ordered pairs to
`(x_(1),y_(1))` and
`(x_(2),y_(2))` and substitute!

`d =\sqrt{(2 -(-3))^(2)+ (3 - (-1))^(2)}`

`d =\sqrt{5^(2)+4^(2)}`

`d =√(25 + 16)`

`d =√(41)` This is equal to approximately 6.40 units.

The last step is to find the perimeter. To find the perimeter, add of the three sides of the triangle together.

P = 5 units + 4 units + 6.4 units

P = 15.4 units

Therefore, the perimeter of this triangle is choice A, 15.4.