Finding the Area of a Garden

Question

Use the image to complete the activity.
1. A square garden has the end points listed below. Plot and label these points on
the grid:
a. A (-7, 6)
b. B (-2, -6)
c. C (10, -1)
d. 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 in
feet.

Answer 1

To find the side length of Square ABCD, we can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula is √[(x2 - x1)^2 + (y2 - y1)^2].

For side AB:
x1 = -7, y1 = 6 (point A)
x2 = -2, y2 = -6 (point B)

Using the distance formula, we have AB = √[(-2 - (-7))^2 + (-6 - 6)^2]
= √[5^2 + (-12)^2]
= √[25 + 144]
= √169
= 13 feet

For side BC:
x1 = -2, y1 = -6 (point B)
x2 = 10, y2 = -1 (point C)

Using the distance formula, we have BC = √[(10 - (-2))^2 + (-1 - (-6))^2]
= √[12^2 + 5^2]
= √[144 + 25]
= √169
= 13 feet

For side CD:
x1 = 10, y1 = -1 (point C)
x2 = 5, y2 = 11 (point D)

Using the distance formula, we have CD = √[(5 - 10)^2 + (11 - (-1))^2]
= √[(-5)^2 + 12^2]
= √[25 + 144]
= √169
= 13 feet

For side DA:
x1 = 5, y1 = 11 (point D)
x2 = -7, y2 = 6 (point A)

Using the distance formula, we have DA = √[(-7 - 5)^2 + (6 - 11)^2]
= √[(-12)^2 + (-5)^2]
= √[144 + 25]
= √169
= 13 feet

Since all sides of Square ABCD have the same length of 13 feet, the side length, s, of Square ABCD is 13 feet.