Question

A parallelogram has vertices D(2, 1), E(2, 6), F(5, 6), G(5 , 1). Determine whether DEFG is a rhombus, rectangle, both, or neither. Explain your reasoning.

Thank you!!!

Answer 1

The parallelogram is a rectangle.

Explanation:

You can tell this by looking at the change in the x values on the top and bottom. Where y = 1, we look at the x changes.

5 - 2 = 3

Same where y = 6

5 - 2 = 3

So, we know the top and bottom to be equal to 3. Next we look at the change in y values to determine the side lengths. In both cases, we get 5.

6 - 1 = 5

6 - 1 = 5

Therefore, it must be a rectangle.