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: $d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

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.

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

$d =\sqrt{5^{2}+0^{2}}$

$d =\sqrt{25} = 5$

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.

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

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

$d =\sqrt{16} = 4$

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!

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

$d =\sqrt{5^{2}+4^{2}}$

$d =\sqrt{25 + 16}$

$d =\sqrt{41}$ 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.