Question

graph the image of △klm after a rotation 180° clockwise around the origin.

Explanation:

Step1: Find coordinates of K, L, M

From the graph: \( K(-1, -9) \), \( L(5, -9) \), \( M(2, -7) \)

Step2: Apply 180° rotation rule

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

• For \( K(-1, -9) \): \( (-(-1), -(-9)) = (1, 9) \)
• For \( L(5, -9) \): \( (-5, -(-9)) = (-5, 9) \)
• For \( M(2, -7) \): \( (-2, -(-7)) = (-2, 7) \)

Step3: Plot the new points

Plot \( K'(1, 9) \), \( L'(-5, 9) \), \( M'(-2, 7) \) and connect them to form the rotated triangle.

Answer:

The image of \( \triangle KLM \) after \( 180^\circ \) clockwise rotation around the origin has vertices at \( K'(1, 9) \), \( L'(-5, 9) \), and \( M'(-2, 7) \). (Graph by plotting these points and connecting them.)