Question

graph the image of $\triangle klm$ after a rotation $180{}^{\circ }$ clockwise around the origin.

Explanation:

Step1: Find the coordinates of \( \triangle KLM \)

Assume \( K(0, - 9) \), \( L(7, - 9) \), \( M(2, - 7) \)

Step2: Apply the rotation rule

The rule for a \( 180^{\circ} \) clockwise rotation around the origin is \( (x,y)\to(-x,-y) \)
For point \( K(0, - 9) \): \( (0, - 9)\to(0,9) \)
For point \( L(7, - 9) \): \( (7, - 9)\to(-7,9) \)
For point \( M(2, - 7) \): \( (2, - 7)\to(-2,7) \)

Step3: Plot the new points

Plot the points \( K'(0,9) \), \( L'(-7,9) \), \( M'(-2,7) \) and connect them to form the image of \( \triangle KLM \) after a \( 180^{\circ} \) clockwise rotation.

Answer:

Plot the points \( (0,9) \), \( (-7,9) \), \( (-2,7) \) and connect them.