To plot and label the points on the grid, you can use a coordinate grid with the x-axis representing the horizontal values and the y-axis representing the vertical values. Each point will be plotted as (x, y).
a. A (-7, 6): Plot a point at (-7, 6).
b. B (-2, -6): Plot a point at (-2, -6).
c. C (10, -1): Plot a point at (10, -1).
d. D (5, 11): Plot a point at (5, 11).
Next, you can connect the points to create Square ABCD. Connect point A to point B, B to C, C to D, and D back to A.
To find the side length, s, of Square ABCD, you can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, since Square ABCD is a square, all sides are equal.
To find the side length, you can calculate the distance between any two adjacent points using the distance formula:
d = β[(x2 - x1)^2 + (y2 - y1)^2]
Using points A (-7, 6) and B (-2, -6) as an example:
d = β[(-2 - (-7))^2 + (-6 - 6)^2]
= β[(-2 + 7)^2 + (-6 - 6)^2]
= β[5^2 + (-12)^2]
= β[25 + 144]
= β169
= 13
So the side length, s, of Square ABCD is 13 feet.
To find the area of Square ABCD, you can use the area formula A = s^2, where s is the side length.
A = 13^2
= 169 square feet.