Question

A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?

On a coordinate plane, a rectangle has points D prime (negative 1, 3), E prime (4, 3), F prime (4, 1), G prime (negative 1, 1).

On a coordinate plane, a rectangle has points D prime (negative 2, 5), E prime (3, 5), F prime (3, 3), G prime (negative 2, 3).

On a coordinate plane, a rectangle has points D prime (0, 2), E prime (5, 2), F prime (5, 0), G prime (0, 0).

On a coordinate plane, a rectangle has points D prime (negative 1, negative 1), E prime (4, negative 1), F prime (4, negative 3), G prime (negative 1, negative 3).

Answer 1

To find the image of rectangle DEFG when translated using \( T_{-1, 2}(x, y) \), we need to apply the translation transformation to each of the vertices of the rectangle.

The translation \( T_{-1, 2}(x, y) \) shifts each point \( (x, y) \) to a new location given by:

\[
(x', y') = (x - 1, y + 2)
\]

Now, let's apply this translation to each of the points:

1. For point D(-1, 3):
\[
D' = (-1 - 1, 3 + 2) = (-2, 5)
\]

2. For point E(4, 3):
\[
E' = (4 - 1, 3 + 2) = (3, 5)
\]

3. For point F(4, 1):
\[
F' = (4 - 1, 1 + 2) = (3, 3)
\]

4. For point G(-1, 1):
\[
G' = (-1 - 1, 1 + 2) = (-2, 3)
\]

After applying the translation, the new coordinates are:
- D'(-2, 5)
- E'(3, 5)
- F'(3, 3)
- G'(-2, 3)

Thus, the image of rectangle DEFG after the translation is:
- D'(-2, 5)
- E'(3, 5)
- F'(3, 3)
- G'(-2, 3)

The coordinates that match this translation correspond to the option:
**On a coordinate plane, a rectangle has points D prime (negative 2, 5), E prime (3, 5), F prime (3, 3), G prime (negative 2, 3).**