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.
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, π΄π΄ = π π 2, to find the area of Square ABCD.
A = ________feet
3 answers
Screen Diagonal Width Height
A 15β 13β
B 22β 19β
C 32β 28β
D 40β 35β
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 Yoselinβs shelf?
A 15β 13β
B 22β 19β
C 32β 28β
D 40β 35β
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 Yoselinβs 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 = β225
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 = β56
b β 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 = β484
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 = β123
b β 11.09 inches
So, the height of screen B is approximately 11.09 inches.
c. For screen C:
c^2 = 32^2
c = β1024
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 = β240
b β 15.49 inches
So, the height of screen C is approximately 15.49 inches.
d. For screen D:
c^2 = 40^2
c = β1600
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 = β375
b β 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.
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 = β225
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 = β56
b β 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 = β484
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 = β123
b β 11.09 inches
So, the height of screen B is approximately 11.09 inches.
c. For screen C:
c^2 = 32^2
c = β1024
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 = β240
b β 15.49 inches
So, the height of screen C is approximately 15.49 inches.
d. For screen D:
c^2 = 40^2
c = β1600
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 = β375
b β 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.