Question

You design a tree house using a coordinate plane. You plot the vertices of the floor at J(2,1), K(2,8), L(9,8), and M(9,1). The coordinates are measured in feet. Which best describes the shape of the floor?

a) Triangle
b) Square
c) Trapezoid
d) A rectangle having a length one foot longer than its width.

Answer 1

The floor of the tree house is a square since all sides are equal in length; each side measures 7 feet.

Step-by-step explanation:

You asked which best describes the shape of the floor for your tree house, with vertices at J(2,1), K(2,8), L(9,8), and M(9,1). By examining the coordinates, we see that the opposite sides are parallel and of equal length. The side JK is parallel to LM since they have the same x-coordinate, and the sides JL and KM are parallel since they share the same y-coordinate. Also, the length of JK and LM (which is 8 - 1 = 7 feet) is equal, and the length of JL and KM (9 - 2 = 7 feet) is equal. This information confirms that the shape is a rectangle where all sides are of equal length, making option (b) Square incorrect. The tree house floor is not a triangle or trapezoid, so options (a) and (c) are incorrect as well. Lastly, the lengths of the sides tell us that the length is equal to the width, and not one foot longer, making option (d) incorrect.

Therefore, the correct answer is that the shape of the tree house floor is a square because all sides are of equal length.