Use the Pythagorean theorem to find the side length s of square A (-7,6) B (-2,-6) C (10,-1) D (5,11)

Answer 1

To find the side length of square A, we can use the distance formula to find the lengths of the sides of the square and then apply the Pythagorean theorem.

First, let's find the lengths of the sides of the square using the distance formula.

The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)

Between points A and B:
d_AB = √((-2 - (-7))^2 + (-6 - 6)^2)
= √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13

Between points B and C:
d_BC = √((10 - (-2))^2 + (-1 - (-6))^2)
= √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13

Between points C and D:
d_CD = √((5 - 10)^2 + (11 - (-1))^2)
= √((-5)^2 + 12^2)
= √(25 + 144)
= √169
= 13

Between points D and A:
d_DA = √((-7 - 5)^2 + (6 - 11)^2)
= √((-12)^2 + (-5)^2)
= √(144 + 25)
= √169
= 13

Now that we have the lengths of all sides, we can see that all of them are equal to 13, which means that all sides of square A have a length of 13 units.