California

Question

Nadia, Brandon, Kelsey, Sophia, and Miguel have designed a garden landscape and each is digging his or her own garden. Kelsey has already dug her garden, DEFG. The coordinates of its vertices are: D (⁺5,⁺7), E (⁺9,⁺7), F (⁺8,⁺2), G (⁺6,⁺2).

• Nadia's garden is a right triangle, ABC.
• The right angle of her garden is 4 units left of vertex G of Kelsey's garden.
• Vertex A of Nadia's garden is up 5 units from the right angle.
• Vertex B of Nadia's garden is right 3 units from the right angle.
• Brandon's garden is a reflection of Kelsey's garden across the x-axis. It is labeled MNOP.
• Sophia's garden is a reflection of Nadia's garden across the y-axis. It is labeled JKL.
• Miguel's garden is a translation of Nadia's garden 6 units to the left and 9 units down. It is labeled XYZ.

What are the coordinates of each person's garden?
On the grid, draw each garden labeled with its coordinates and each person's name.