Question

graph quadrilateral $jklm$ and its image after a rotation $180^{circ}$ about the origin.

Explanation:

Step1: Find coordinates of original points

Assume \( J(1,4) \), \( K(6,6) \), \( L(7,2) \), \( M(1,2) \).

Step2: Apply rotation rule

The rule for a \( 180^{\circ} \) rotation about the origin is \( (x,y)\to(-x,-y) \).
For \( J(1,4) \): \( (1,4)\to J'(-1,-4) \).
For \( K(6,6) \): \( (6,6)\to K'(-6,-6) \).
For \( L(7,2) \): \( (7,2)\to L'(-7,-2) \).
For \( M(1,2) \): \( (1,2)\to M'(-1,-2) \).

Step3: Graph the original and new points

Plot \( J(1,4) \), \( K(6,6) \), \( L(7,2) \), \( M(1,2) \) for quadrilateral \( JKLM \). Plot \( J'(-1,-4) \), \( K'(-6,-6) \), \( L'(-7,-2) \), \( M'(-1,-2) \) for the rotated quadrilateral.

Answer:

Graph \( JKLM \) with vertices \( J(1,4) \), \( K(6,6) \), \( L(7,2) \), \( M(1,2) \) and its image after \( 180^{\circ} \) rotation \( J'(-1,-4) \), \( K'(-6,-6) \), \( L'(-7,-2) \), \( M'(-1,-2) \) by connecting the respective points.