Use the given coordinates to compute the perimeter of the parallelogram. (1 point) Responses 25.2 units 25.2 units 28 units 28 units 26.6 units 26.6 units 13.3 unitsd9d/MAGEOM0062_N_F10.png

Answer 1

To calculate the perimeter of a parallelogram, you generally need the lengths of two adjacent sides. The formula for the perimeter \( P \) of a parallelogram is given by:

\[ P = 2(a + b) \]

where \( a \) is the length of one side and \( b \) is the length of the adjacent side.

However, to determine the side lengths from coordinates, you need to find the distances between given points. Assuming you have the coordinates of the vertices of the parallelogram, let's denote them as:

• \( A(x_1, y_1) \)
• \( B(x_2, y_2) \)
• \( C(x_3, y_3) \)
• \( D(x_4, y_4) \)

You would find the lengths of the sides using the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

The sides of the parallelogram are typically \( AB \) and \( AD \) or any pairing of opposite sides.

Without specific coordinates, I can't calculate the perimeter directly. If you can provide the coordinates or clarify, I can help you determine the perimeter accurately.

Based on the responses provided, if the calculated lengths of the two adjacent sides ended up to be 13.3 units and 25.2 units, the perimeter would be calculated as:

\[ P = 2(13.3 + 25.2) = 2(38.5) = 77 \text{ units} \]

Please check and follow up with the specific coordinates for more accuracy!

Answer 2

Use the coordinates to compute the perimeter of the trapezoid. Round each calculation to the nearest tenth. (1 point) Responses 12.3 units 12.3 units 13.8 units 13.8 units 14.4 units 14.4 units 16.3 units

Answer 3

To calculate the perimeter of a trapezoid using its coordinates, you will first need the coordinates of the four vertices of the trapezoid, which we'll denote as \( A(x_1, y_1) \), \( B(x_2, y_2) \), \( C(x_3, y_3) \), and \( D(x_4, y_4) \).

The perimeter \( P \) can be calculated using the distances between each pair of adjacent vertices:

\[ P = AB + BC + CD + DA \]

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) can be found using the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

You will need to compute the lengths for each side of the trapezoid:

1. Calculate \( AB \)
2. Calculate \( BC \)
3. Calculate \( CD \)
4. Calculate \( DA \)

Finally, sum these lengths to find the total perimeter, rounding each side length calculation to the nearest tenth.

As you have not provided the specific coordinates, I cannot perform the exact calculations. If you can provide the coordinates for the vertices, I could assist in calculating the perimeter step by step.

If you find the answers provided in your options (12.3 units, 13.8 units, 14.4 units, and 16.3 units) relate to possible values of perimeter based on the lengths you calculate, then you can check which one is correct based on your calculations.

Answer 4

Use the image to answer the question. Use the coordinates to compute the perimeter of the triangle. (1 point) Responses 10.8 units 10.8 units 12 units 12 units 11.2 units 11.2 units 10 units

Answer 5

To compute the perimeter of a triangle using its vertices' coordinates, you'll need to calculate the lengths of all three sides using the distance formula. The perimeter \( P \) is then the sum of these lengths.

Steps:

1. Identify the Coordinates: Assuming you denote the triangle's vertices as \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \).

2. Calculate Side Lengths:

   • For side \( AB \): \[ d_{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

   • For side \( BC \): \[ d_{BC} = \sqrt{(x_3 - x_2)^2 + (y_3 - y_2)^2} \]

   • For side \( CA \): \[ d_{CA} = \sqrt{(x_1 - x_3)^2 + (y_1 - y_3)^2} \]

3. Add Lengths to Find Perimeter: \[ P = d_{AB} + d_{BC} + d_{CA} \]

Example Calculation

Since I don’t have the actual coordinates from the image, here's an example with a hypothetical set of coordinates:

• \( A(1, 2) \)
• \( B(4, 6) \)
• \( C(7, 2) \)

Calculating Lengths:

• Length of \( AB \): \[ d_{AB} = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

• Length of \( BC \): \[ d_{BC} = \sqrt{(7 - 4)^2 + (2 - 6)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

• Length of \( CA \): \[ d_{CA} = \sqrt{(1 - 7)^2 + (2 - 2)^2} = \sqrt{(-6)^2 + 0^2} = \sqrt{36} = 6 \]

Perimeter:

\[ P = 5 + 5 + 6 = 16 \]

Please use your specific coordinates from the image to perform the calculations similarly, and then compare your result with the perimeter options provided (10.8 units, 12 units, 11.2 units, 10 units) to find the correct answer. If you share the coordinates, I can help with exact calculations!