Question

graph the image of rectangle vwxy after the following sequence of transformations: rotation 270° counterclockwise around the origin translation 1 unit right and 15 units down

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of rectangle \( VWXY \):

• \( V(-6, 11) \)
• \( W(-11, 5) \)
• \( X(-8, 2) \)
• \( Y(-2, 8) \)

Step2: Apply 270° counterclockwise rotation

The rule for a \( 270^\circ \) counterclockwise rotation around the origin is \( (x, y) \to (y, -x) \).

• For \( V(-6, 11) \): \( (11, 6) \)
• For \( W(-11, 5) \): \( (5, 11) \)
• For \( X(-8, 2) \): \( (2, 8) \)
• For \( Y(-2, 8) \): \( (8, 2) \)

Step3: Apply translation (1 unit right, 15 units down)

The translation rule is \( (x, y) \to (x + 1, y - 15) \).

• For \( V' (11, 6) \): \( (11 + 1, 6 - 15) = (12, -9) \)
• For \( W' (5, 11) \): \( (5 + 1, 11 - 15) = (6, -4) \)
• For \( X' (2, 8) \): \( (2 + 1, 8 - 15) = (3, -7) \)
• For \( Y' (8, 2) \): \( (8 + 1, 2 - 15) = (9, -13) \)

Step4: Graph the new vertices

Plot the points \( (12, -9) \), \( (6, -4) \), \( (3, -7) \), and \( (9, -13) \) and connect them to form the image of the rectangle after the transformations.

Answer:

The image of rectangle \( VWXY \) after the transformations has vertices at \( (12, -9) \), \( (6, -4) \), \( (3, -7) \), and \( (9, -13) \). (Graphing these points on the coordinate plane will show the transformed rectangle.)