Question

graph the image of rectangle klmn after a rotation 180° clockwise around the origin.

Explanation:

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

From the graph, let's assume the coordinates:

• \( K(0, -10) \)
• \( L(1, -10) \)
• \( M(1, -3) \)
• \( N(0, -3) \)

Step2: Apply 180° rotation rule

The rule for a 180° clockwise (or counterclockwise) rotation around the origin is \((x, y) \to (-x, -y)\).

For \( K(0, -10) \):
\( (0, -10) \to ( -0, -(-10)) = (0, 10) \) (new \( K' \))

For \( L(1, -10) \):
\( (1, -10) \to (-1, -(-10)) = (-1, 10) \) (new \( L' \))

For \( M(1, -3) \):
\( (1, -3) \to (-1, -(-3)) = (-1, 3) \) (new \( M' \))

For \( N(0, -3) \):
\( (0, -3) \to ( -0, -(-3)) = (0, 3) \) (new \( N' \))

Step3: Plot the new points

Plot \( K'(0, 10) \), \( L'(-1, 10) \), \( M'(-1, 3) \), \( N'(0, 3) \) and connect them to form the rotated rectangle.

Answer:

The image of rectangle \( KLMN \) after a 180° clockwise rotation around the origin has vertices at \( K'(0, 10) \), \( L'(-1, 10) \), \( M'(-1, 3) \), and \( N'(0, 3) \). (To graph, plot these points and draw the rectangle.)