Question

The points I (−4,5), J (−4,−3), K (5,−8), and L (5,0) form the parallelogram IJKL. Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter of the parallelogram. Round your answer to the nearest tenth if necessary.

Perimeter- .... units

Answer 1

Answer: To find the perimeter of a parallelogram, we need to find the lengths of its sides. The sides of the parallelogram can be determined by calculating the distance between the given points.

Using the distance formula, the lengths of the sides can be calculated as follows:

Side IJ:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((-4 - (-4))^2 + (-3 - 5)^2)

Distance = √(0^2 + (-8)^2)

Distance = √(0 + 64)

Distance = √64

Distance = 8

Side JK:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((5 - (-4))^2 + (-8 - (-3))^2)

Distance = √((5 + 4)^2 + (-8 + 3)^2)

Distance = √(9^2 + (-5)^2)

Distance = √(81 + 25)

Distance = √106

Distance ≈ 10.3 (rounded to the nearest tenth)

Side KL:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((5 - 5)^2 + (0 - (-8))^2)

Distance = √(0^2 + 8^2)

Distance = √(0 + 64)

Distance = √64

Distance = 8

Side LI:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((-4 - 5)^2 + (5 - 0)^2)

Distance = √((-9)^2 + 5^2)

Distance = √(81 + 25)

Distance = √106

Distance ≈ 10.3 (rounded to the nearest tenth)

Now, we can calculate the perimeter by adding up the lengths of all four sides:

Perimeter = IJ + JK + KL + LI

Perimeter = 8 + 10.3 + 8 + 10.3

Perimeter ≈ 36.6 (rounded to the nearest tenth)

Therefore, the perimeter of the parallelogram IJKL is approximately 36.6 units.