# Landscape Locations

## Solution

Given:
Kelsey's garden is DEFG. The coordinates of its vertices are: D (+5,+7), E (+9,+7), F (+8,+2), G (+6,+2).
The other gardens:
Nadia's garden is a right triangle, ABC. The coordinates of its vertices are:
A (+2,+7), B (+5,+2), C (+2,+2).
Brandon's garden is MNOP. The coordinates of its vertices are:
M (+5,7), N (+9,7), O (+8,2), P (+6,2).
Sophia's garden is a right triangle, JKL. The coordinates of its vertices are:
J (2,+7), K (5,+2), L (2,+2).
Miguel's garden is a right triangle, XYZ. The coordinates of its vertices are:
X (4,2), Y (1,7), Z (4,7).

## Explanation

Kelsey's garden is 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.
Since the vertices for the other angles are given as A and B, the right angle must be C.
Vertex G of Kelsey's garden is (+6,+2).
Translate 4 units to the left: (+6,+2) → (+2,+2).
The right angle C is (+2,+2).
Vertex A of Nadia's garden is up 5 units from the right angle.
Up 5 from (+2,+2) is (+2,+7)
Vertex B of Nadia's garden is right 3 units from the right angle.
Right 3 units from (+2,+2) is (+5,+2).
The coordinates of its vertices are: A (+2,+7), B (+5,+2),
C (+2,+2).

Brandon's garden is a reflection of Kelsey's garden across the x-axis.
It is labeled MNOP.
The coordinates of the vertices of Kelsey's garden are D (+5,+7), E (+9,+7), F (+8,+2), G (+6,+2).
To reflect each vertex across the x-axis, plot the same x-coordinates and the opposite y-coordinates:
(+5,7), (+9,7), (+8,2), G (+6,2).
Brandon's garden is MNOP. The coordinates of its vertices are:
M (+5,7), N (+9,7), O (+8,2), P (+6,2).

Sophia's garden is a reflection of Nadia's garden across the y-axis.
It is labeled JKL.
The coordinates of Nadia's garden are: A (+2,+7), B (+5,+2), C (+2,+2).
To reflect each vertex across the y-axis, plot the opposite x-coordinates and the same y-coordinates:
(2,+7), (5,+2), (2,+2).
Sophia's garden is JKL. Its coordinates are J (2,+7), K (5,+2), L (2,+2).

Miguel's garden is a translation of Nadia's garden 6 units to the left and 9 units down. It is labeled XYZ.
Begin with the vertices of Nadia's garden: A (+2,+7), B (+5,+2), C (+2,+2).
Translate each 6 units to the left and 9 units down.
A (+2,+7) → (-4,2)
B (+5,+2) → (-1,-7)
C (+2,+2) → (-4,-7)
Miguel's garden is a right triangle, XYZ. The coordinates of its vertices are: X (-4,-2), Y (-1,-7), Z (-4,-7).