Question

graph the image of rectangle klmn after a rotation 90° clockwise around the origin.

Explanation:

Step1: Find coordinates of K, L, M, N

From the graph:

• \( K(4, 2) \)
• \( L(8, 2) \)
• \( M(8, 10) \)
• \( N(4, 10) \)

Step2: Apply 90° clockwise rotation rule

The rule for a 90° clockwise rotation about the origin \((x, y) \to (y, -x)\).

• For \( K(4, 2) \):

New coordinates: \( (2, -4) \)

• For \( L(8, 2) \):

New coordinates: \( (2, -8) \)

• For \( M(8, 10) \):

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

• For \( N(4, 10) \):

New coordinates: \( (10, -4) \)

Step3: Plot the new points

Plot \( K'(2, -4) \), \( L'(2, -8) \), \( M'(10, -8) \), \( N'(10, -4) \) and connect them to form the rotated rectangle.

Answer:

The image of rectangle \( KLMN \) after a 90° clockwise rotation around the origin has vertices at \( K'(2, -4) \), \( L'(2, -8) \), \( M'(10, -8) \), and \( N'(10, -4) \). (Plot these points on the coordinate plane to see the rotated rectangle.)