Question

pca activity sheet for the week of 12/8/2025
monday: pca: choose the best answer.
polygon klmn is the image of polygon pqrsafter a 180° rotation.

Explanation:

Step1: Recall 180° rotation rule

For a point \((x,y)\), a \(180^\circ\) rotation about the origin gives \((-x,-y)\).

Step2: Find coordinates of PQRS

• \(P(-4,3)\), \(Q(-6,3)\), \(R(-7,6)\), \(S(-5,8)\)

Step3: Apply rotation to each point

• \(P(-4,3)\to K(4,-3)\)
• \(Q(-6,3)\to L(6,-3)\)
• \(R(-7,6)\to M(7,-6)\)
• \(S(-5,8)\to N(5,-8)\)

Step4: Plot or identify KLMN

Using the rotated coordinates, KLMN will have vertices at \((4,-3)\), \((6,-3)\), \((7,-6)\), \((5,-8)\), which is the image below the x - axis, symmetric to PQRS about the origin.

Answer:

The coordinates of KLMN are \(K(4, - 3)\), \(L(6, - 3)\), \(M(7, - 6)\), \(N(5, - 8)\) (or the polygon formed by these points on the grid).