Question

I am an 8th grade student and am struggling with finding the solution to this problem. erg! Help please? Thanks in advance

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)

Connect the points to create Square ABCD.

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

Area = a2 + b2 = c2 where c is the side length, s.

s = feet

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

A = feet

Answer 1

The side length of Square ABCD is 13 feet, and its area is 169 square feet.

To plot Square ABCD, we connect the given points A(-7, 6), B(-2, -6), C(10, -1), and D(5, 11) on the coordinate grid. Connecting these points forms a square.

Now, let's find the side length (s) of Square ABCD using the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

We can consider AB, BC, CD, and DA as the sides of the square:

Side AB: s_AB = √(((-2) - (-7))^2 + ((-6) - 6)^2) = √(5^2 + (-12)^2) = √(25 + 144) = √169 = 13

Side BC: s_BC = √((10 - (-2))^2 + ((-1) - (-6))^2) = √(12^2 + 5^2) = √(144 + 25) = √169 = 13

Side CD: s_CD = √((5 - 10)^2 + (11 - (-1))^2) = √((-5)^2 + 12^2) = √(25 + 144) = √169 = 13

Side DA: s_DA = √(((-7) - 5)^2 + (6 - 11)^2) = √((-12)^2 + (-5)^2) = √(144 + 25) = √169 = 13

All sides are equal, confirming that ABCD is a square.

Now, using the area formula A = s^2, the area of Square ABCD is A = 13^2 = 169 square feet.