Question

graph the image of rectangle efgh after a rotation 270° clockwise around the origin.

Explanation:

Step1: Find coordinates of E, F, G, H

From the graph:

• \( E(1, 2) \)
• \( F(10, 2) \)
• \( G(10, 8) \)
• \( H(1, 8) \)

Step2: Apply 270° clockwise rotation rule

The rule for rotating a point \((x, y)\) 270° clockwise around the origin is \((x, y) \to (y, -x)\).

• For \( E(1, 2) \):

New coordinates: \( (2, -1) \)

• For \( F(10, 2) \):

New coordinates: \( (2, -10) \)

• For \( G(10, 8) \):

New coordinates: \( (8, -10) \)

• For \( H(1, 8) \):

New coordinates: \( (8, -1) \)

Step3: Plot the new points

Plot \( E'(2, -1) \), \( F'(2, -10) \), \( G'(8, -10) \), \( H'(8, -1) \) and connect them to form the rotated rectangle.

(Note: Since the task is to graph, the final answer involves plotting these points. The key is applying the rotation rule to each vertex.)

Answer:

Step1: Find coordinates of E, F, G, H

From the graph:

• \( E(1, 2) \)
• \( F(10, 2) \)
• \( G(10, 8) \)
• \( H(1, 8) \)

Step2: Apply 270° clockwise rotation rule

The rule for rotating a point \((x, y)\) 270° clockwise around the origin is \((x, y) \to (y, -x)\).

• For \( E(1, 2) \):

New coordinates: \( (2, -1) \)

• For \( F(10, 2) \):

New coordinates: \( (2, -10) \)

• For \( G(10, 8) \):

New coordinates: \( (8, -10) \)

• For \( H(1, 8) \):

New coordinates: \( (8, -1) \)

Step3: Plot the new points

Plot \( E'(2, -1) \), \( F'(2, -10) \), \( G'(8, -10) \), \( H'(8, -1) \) and connect them to form the rotated rectangle.

(Note: Since the task is to graph, the final answer involves plotting these points. The key is applying the rotation rule to each vertex.)