Question

describe a congruence transformation that maps the blue preimage to the green image. a 270° rotation about the origin a reflection in the line y = -1 a reflection in the line y = -x a 180° rotation about the origin

Explanation:

Step1: Identify coordinates of preimage

Take point W(-5,5), X(-3,5), Y(-2,3), Z(-5,3) (blue shape).

Step2: Test 180° rotation rule

180° rotation: (x,y)→(-x,-y). Apply to W: (-(-5), -5)=(5,-5); X: (-(-3),-5)=(3,-5); Y: (-(-2),-3)=(2,-3); Z: (-(-5),-3)=(5,-3). These match green shape's coordinates (R(2,-3), S(3,-5), P(5,-5), Q(5,-3)).

Step3: Verify other options

270° rotation, reflections in y=-1 or y=-x don’t map blue to green.

Answer:

D. a 180° rotation about the origin