Question

HELP. PLEASE

The coordinates of the vertices of a rectangle are (−3,2), (5,4), (6,0), and (−2,−2)
What is the perimeter of the rectangle, to the nearest tenth of a unit?

8.2 units

12.4 units

24.7 units

34.0 units

Answer 1

If we calculate the distance between two points, it is equivalent to one side of the rectangle. Using the distance formula:
d = √((x₂ - x₁)² + (y₂-y₁)²)
We compute the distance between the points (-3,2) and (5,4)
d = √((5 + 3)² + (4 - 2)²) = √68
Now, we check the next two points:
d = √((6 - 5)² + (0 - 4)² = √17
Now, we know that the adjacent sides of a rectangle are equal so the perimeter can be calculated using:
P = 2(l₁ + l₂)
P = 2(√68 + √17)
=24.7 units.