You can use the Pythagorean Theorem to find the area of a square when you know its end points.

1. A square garden has the end points listed below. Plot and label these points on

the grid:

A(- 7, 6)

B(- 2, - 6)

C(10,- 1)

D(5, 11)

2. Connect the points to create Square ABCD.

3. Use the Pythagorean Theorem to find the side length, s, of Square ABCD.

4. Use the area formula, A = s ^ 2 to find the area of Square ABCD.

1 answer

To find the side length of Square ABCD using the Pythagorean Theorem, we need to calculate the distance between two of the points on the square.

Let's use points A (-7, 6) and B (-2, -6) to find the side length.

Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)

Here, x1 = -7, y1 = 6, x2 = -2, and y2 = -6.

Applying the formula:
d = √((-2 - (-7))^2 + (-6 - 6)^2)
= √((5)^2 + (-12)^2)
= √(25 + 144)
= √169
= 13

Therefore, the side length of Square ABCD is 13 units.

To find the area of Square ABCD, we can use the formula A = s^2, where s is the side length.

Using s = 13, we have:
A = 13^2
A = 169 square units

The area of Square ABCD is 169 square units.