1. EXAMPLE 1
Translate a figure in the coordinate plane
Graph quadrilateral ABCD with vertices A(–1, 2), B(–1, 5), C(4, 6), and D(4, 2). Find the image of each vertex after the translation (x, y) →(x + 3, y – 1). Then graph the image using prime notation.
SOLUTION
First, draw ABCD. Find the translation of each vertex by adding 3 to its x-coordinate and subtracting 1 from its y-coordinate. Then graph the image.

2. EXAMPLE 1
Translate a figure in the coordinate plane
Graph quadrilateral ABCD with vertices A(–1, 2), B(–1, 5), C(4, 6), and D(4, 2). Find the image of each vertex after the translation (x, y) →(x + 3, y – 1). Then graph the image using prime notation.
(x, y) → (x + 3, y – 1)
A(–1, 2) → A′(2, 1)
B(–1, 5) → B′(2, 4)
C(4, 6) → C′(7, 5)
D(4, 2) → D′(7, 1)

3. GUIDED PRACTICE
for Example 1 1.
Draw RST with vertices R(2, 2), S(5, 2), and T(3, 5). Find the image of each vertex after the translation (x, y) → (x + 1, y + 2). Graph the image using prime notation.
SOLUTION
First, draw Find the translation of each vertex by adding 1 to its x-coordinate and adding 2 to its y-coordinate. Then graph the image.
RST

4. GUIDED PRACTICE
for Example 1
Graph triangle RST with vertices R(2, 2), S(5, 2), T(3, 5). Find the image of each vertex after the translation (x, y) →(x + 1, y + 2). Then graph the image using prime notation.
(x, y) → (x + 1, y + 2) y R S T ′ x
R(2, 2) → R′(3, 4)
S(5, 2) → S′(6, 4)
T(3, 5) → T′(4, 7)

5. GUIDED PRACTICE
for Example 1 2.
The image of (x, y) → (x + 4, y – 7) is P′Q′ with endpoints P′(–3, 4) and Q′(2, 1). Find the coordinates of the endpoints of the preimage.
SOLUTION
To find the
coordinates of the endpoints of the
subtract 4 from x-coordinate and add
preimage
7 to y-coordinate.
(x, y) → (x – 4, y + 7)
P'( 3, 4) → P(– 7, 11) –
Q'(2, 1) → Q(– 2, 8)