You design a tree house using a coordinate plane. You plot the vertices of the floor at J(1, 1), K(1, 9), L(9, 9), and M(9, 1). The coordinates are measured in feet. What is the perimeter of the tree house?Question 23Select one:a.30 feetb.28 feetc.32 feetd.64 feet
Question
You design a tree house using a coordinate plane. You plot the vertices of the floor at J(1, 1), K(1, 9), L(9, 9), and M(9, 1). The coordinates are measured in feet. What is the perimeter of the tree house?Question 23Select one:a.30 feetb.28 feetc.32 feetd.64 feet
Solution
The perimeter of a shape is the sum of the lengths of all its sides.
In this case, the tree house floor is a square with vertices at J(1, 1), K(1, 9), L(9, 9), and M(9, 1).
The distance between two points (x1, y1) and (x2, y2) on a coordinate plane can be found using the distance formula: √[(x2-x1)² + (y2-y1)²].
- Calculate the distance between J and K: √[(1-1)² + (9-1)²] = √[0 + 64] = 8 feet
- Calculate the distance between K and L: √[(9-1)² + (9-9)²] = √[64 + 0] = 8 feet
- Calculate the distance between L and M: √[(9-9)² + (9-1)²] = √[0 + 64] = 8 feet
- Calculate the distance between M and J: √[(1-9)² + (1-1)²] = √[64 + 0] = 8 feet
Add up all the sides to get the perimeter: 8 feet + 8 feet + 8 feet + 8 feet = 32 feet
So, the correct answer is c. 32 feet.
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