(A coordinate plane)
One friend wants an L-shaped flower bed. They want the
coordinates for the vertices to be:
A (-2, -4), B (-2, 6), C (0, 6), D (0, -2), E (3, -2), and F (3, -4)
1. Plot the points on the coordinates grid in alphabetical order and
connect the points to make an L-shaped figure
2. If length is measured in feet, what is the perimeter of the flower bed?
Show your work!
1. The points on the coordinate plane are as follows:
A (-2, -4), B (-2, 6), C (0, 6), D (0, -2), E (3, -2), and F (3, -4)
Connecting the points in alphabetical order, we get the following L-shaped figure:
A (-2, -4) --- D (0, -2) --- E (3, -2)
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B (-2, 6) --- C (0, 6)
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F (3, -4)
2. To find the perimeter of the flower bed, we need to calculate the sum of the lengths of all the sides of the L-shaped figure.
Side AB: sqrt[(-2 - (-2))^2 + (6 - (-4))^2] = sqrt[0^2 + 10^2] = sqrt(100) = 10 feet
Side BC: sqrt[(0 - (-2))^2 + (6 - 6)^2] = sqrt[2^2 + 0^2] = sqrt(4) = 2 feet
Side CD: sqrt[(0 - 0)^2 + (-2 - 6)^2] = sqrt[0^2 + (-8)^2] = sqrt(64) = 8 feet
Side DE: sqrt[(3 - 0)^2 + (-2 - (-2))^2] = sqrt[3^2 + 0^2] = sqrt(9) = 3 feet
Side EF: sqrt[(3 - 3)^2 + (-4 - (-2))^2] = sqrt[0^2 + (-2)^2] = sqrt(4) = 2 feet
Side FA: sqrt[(-2 - 3)^2 + (-4 - (-4))^2] = sqrt[(-5)^2 + 0^2] = sqrt(25) = 5 feet
Adding up all the sides:
Perimeter = 10 + 2 + 8 + 3 + 2 + 5 = 30 feet
Therefore, the perimeter of the flower bed is 30 feet.