use the Pythagorean theorem to find the side length, s, of square ABCD in feet.
(the plots of the square are:
a; -7, 6
b; -2, -6
c; 10, -1
d; 5, 11
To use the Pythagorean theorem to find the side length of square ABCD, we need to find the distance between two adjacent vertices of the square. Let's consider the distance between vertex A (-7, 6) and vertex B (-2, -6).
Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates for A (-7, 6) and B (-2, -6), we have:
d = √((-2 - (-7))^2 + (-6 - 6)^2)
= √((5)^2 + (-12)^2)
= √(25 + 144)
= √169
= 13
Therefore, the distance between A and B is 13 feet. Since a square has all sides of equal length, the side length of square ABCD (s) is also 13 feet.
Use the area formula, A = s^2, to find the square area of ABCD
To find the square area of ABCD, we can use the formula A = s^2, where A represents the area and s represents the side length of the square.
From the previous response, we found that the side length of square ABCD is 13 feet.
Plugging in the value of s = 13 into the area formula, we have:
A = (13)^2
= 169 square feet
Therefore, the square area of ABCD is 169 square feet.