Question

graph quadrilateral j k l m and its image after a rotation 180° about the origin

Explanation:

Step1: Find coordinates of original quadrilateral

Assume \(J(1,4)\), \(K(6,5)\), \(L(7,2)\), \(M(2,1)\) (by observing the first graph).

Step2: Apply \(180^{\circ}\) rotation formula

The formula 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 \(K(6,5)\): \((6,5)\to K'(-6,-5)\)
For \(L(7,2)\): \((7,2)\to L'(-7,-2)\)
For \(M(2,1)\): \((2,1)\to M'(-2,-1)\)

Step3: Plot the points

Plot \(J(1,4)\), \(K(6,5)\), \(L(7,2)\), \(M(2,1)\) for quadrilateral \(JKLM\) and \(J'(-1,-4)\), \(K'(-6,-5)\), \(L'(-7,-2)\), \(M'(-2,-1)\) for the rotated image.

Answer:

Plot the original points \(J(1,4)\), \(K(6,5)\), \(L(7,2)\), \(M(2,1)\) and the rotated points \(J'(-1,-4)\), \(K'(-6,-5)\), \(L'(-7,-2)\), \(M'(-2,-1)\) on the coordinate - plane.