help!

Question

Use the Pythagorean Theorem to find the side length, s, of Square ABCD in
feet

s=______feet

SQUARE ABCD IS MADE UP OF
A. (-7, 6)
B. (-2, -6)
C. (10, -1)
D. (5, 11)

ON A COORDINATE GRAPH

Answer 1

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

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

Let's calculate the distances between the consecutive points of Square ABCD:

Distance AB:
d_AB = √((-2 - (-7))^2 + (-6 - 6)^2)
= √(5^2 + (-12)^2)
= √(25 + 144)
= √169
= 13 feet

Distance BC:
d_BC = √((10 - (-2))^2 + (-1 - (-6))^2)
= √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13 feet

Distance CD:
d_CD = √((5 - 10)^2 + (11 - (-1))^2)
= √((-5)^2 + 12^2)
= √(25 + 144)
= √169
= 13 feet

Distance DA:
d_DA = √((-7 - 5)^2 + (6 - 11)^2)
= √((-12)^2 + (-5)^2)
= √(144 + 25)
= √169
= 13 feet

Since all the side lengths are the same and equal to 13 feet, we can conclude that the side length, s, of Square ABCD is 13 feet.