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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.
s = ________feet
4. Use the area formula, 𝐴𝐴 = 𝑠𝑠2, to find the area of Square ABCD.
A = ________feet

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 = √[(x2 - x1)^2 + (y2 - y1)^2]

Using points A (-7, 6) and B (-2, -6) as an example:

d = √[(-2 - (-7))^2 + (-6 - 6)^2]
= √[(-2 + 7)^2 + (-6 - 6)^2]
= √[5^2 + (-12)^2]
= √[25 + 144]
= √169
= 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.

Screen Diagonal Width Height

A 15” 13”
B 22” 19”
C 32” 28”
D 40” 35”
1. Use the Pythagorean Theorem to calculate the height of each screen, and
complete the table.
2. Which screen is the largest that will fit on Yoselin’s shelf?

To calculate the height of each screen using the Pythagorean Theorem, you can use the given screen diagonal width and height.

Using the Pythagorean Theorem (a^2 + b^2 = c^2), where c represents the diagonal, and a and b represent the width and height respectively:

a. For screen A:
c^2 = 15^2
c = √225
c = 15 inches
Using c and the width (a) from the table, we can solve for the height (b):
15^2 = a^2 + b^2
15^2 = 13^2 + b^2
b^2 = 15^2 - 13^2
b^2 = 225 - 169
b^2 = 56
b = √56
b β‰ˆ 7.48 inches
So, the height of screen A is approximately 7.48 inches.

Performing the same calculations for the other screens:

b. For screen B:
c^2 = 22^2
c = √484
c = 22 inches
Using c and the width (a) from the table, we can solve for the height (b):
22^2 = a^2 + b^2
22^2 = 19^2 + b^2
b^2 = 22^2 - 19^2
b^2 = 484 - 361
b^2 = 123
b = √123
b β‰ˆ 11.09 inches
So, the height of screen B is approximately 11.09 inches.

c. For screen C:
c^2 = 32^2
c = √1024
c = 32 inches
Using c and the width (a) from the table, we can solve for the height (b):
32^2 = a^2 + b^2
32^2 = 28^2 + b^2
b^2 = 32^2 - 28^2
b^2 = 1024 - 784
b^2 = 240
b = √240
b β‰ˆ 15.49 inches
So, the height of screen C is approximately 15.49 inches.

d. For screen D:
c^2 = 40^2
c = √1600
c = 40 inches
Using c and the width (a) from the table, we can solve for the height (b):
40^2 = a^2 + b^2
40^2 = 35^2 + b^2
b^2 = 40^2 - 35^2
b^2 = 1600 - 1225
b^2 = 375
b = √375
b β‰ˆ 19.36 inches
So, the height of screen D is approximately 19.36 inches.

To determine which screen is the largest that will fit on Yoselin's shelf, you need to compare the heights of the screens.

Based on the calculated heights:
- Screen A has a height of 7.48 inches.
- Screen B has a height of 11.09 inches.
- Screen C has a height of 15.49 inches.
- Screen D has a height of 19.36 inches.

Therefore, the largest screen that will fit on Yoselin's shelf is screen D with a height of 19.36 inches.

To plot and label the points on the grid, we need to understand their coordinate system. In a Cartesian coordinate system, we have two axes - x and y. The x-axis represents the horizontal distance, and the y-axis represents the vertical distance.

a. Point A is (-7, 6). To plot this point, we move 7 units to the left on the x-axis and 6 units up on the y-axis from the origin (0,0). Thus, we plot Point A at (-7, 6).

b. Point B is (-2, -6). To plot this point, we move 2 units to the left on the x-axis and 6 units down on the y-axis from the origin (0,0). Thus, we plot Point B at (-2, -6).

c. Point C is (10, -1). To plot this point, we move 10 units to the right on the x-axis and 1 unit down on the y-axis from the origin (0,0). Thus, we plot Point C at (10, -1).

d. Point D is (5, 11). To plot this point, we move 5 units to the right on the x-axis and 11 units up on the y-axis from the origin (0,0). Thus, we plot Point D at (5, 11).

Once we have plotted these points on the grid, we can connect them to create Square ABCD.

To find the side length of Square ABCD (let's call it s), we 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, the sides are the horizontal and vertical distances between points.

For the square ABCD, we can consider the sides AB, BC, CD, and DA as the sides of a right triangle. We can calculate the lengths of any two sides and use the Pythagorean Theorem to find the length of the third side.

If we consider sides AB and BC, we can calculate their lengths as follows:

AB = distance between points A and B

To calculate AB, we use the formula: AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates, AB = sqrt((-2 - (-7))^2 + (-6 - 6)^2)

Simplifying, AB = sqrt(5^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13

BC = distance between points B and C

To calculate BC, we use the formula: BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates, BC = sqrt((10 - (-2))^2 + (-1 - (-6))^2)

Simplifying, BC = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13

Since AB = BC = 13, we can conclude that all sides of Square ABCD have a length of 13 feet. Therefore, s = 13 feet.

To calculate the area of Square ABCD, we use the formula A = s^2, where s is the side length.

Substituting the value of s, we get A = 13^2 = 169 square feet.

Therefore, the area of Square ABCD is 169 square feet.