Question

When represented on a coordinate plane a yard has vertices of (0, 0), (3, 4), (6, 0), (3, -4) where each unit on the plane represents 10 feet. What shape is the yard? a. The shape is a rhombus but is not a square. b. The shape is a rectangle but not a square. c. The shape is both a rhombus and a square.

Answer 1

The yard with vertices (0, 0), (3, 4), (6, 0), (3, -4) forms a shape on the coordinate plane that is both a rhombus and a square as it has equal side lengths and angles.

The correct option is c.

Step-by-step explanation:

When the vertices of the yard are plotted on the coordinate plane with points (0, 0), (3, 4), (6, 0), (3, -4), we can examine the properties of the resulting shape to determine its classification.

Since each unit represents 10 feet, the horizontal distance between (0, 0) and (6, 0) is 60 feet, which is equivalent to 20 yards, and the vertical distance between (3, 4) and (3, -4) is also 80 feet or about 26.6 yards.

The equal lengths of the sides and the 90-degree angles between adjacent sides indicate that the shape is both a rhombus (equal side lengths) and a square (equal side lengths and angles).