A square has the vertices below, find the area of the square.

Question

(−7, −5), (−4, −2), (−1, −5), (−4, −8)
(1 point)
Responses

18−−√ square units
18−−√ square units

18 square units
18 square units

6 square units
6 square units

6–√ square units

Answer 1

To find the area of a square, we need to find the length of one side and then square it.

Using the distance formula, we can find the length of one side of the square.

The distance between (-7, -5) and (-4, -2) is:

√((-4 - (-7))^2 + (-2 - (-5))^2)
= √(3^2 + 3^2)
= √(9 + 9)
= √18

Therefore, the length of one side of the square is √18.

To find the area, we square this length:

Area = (√18)^2
= 18

So, the area of the square is 18 square units.