Question

which congruence transformation maps the blue preimage to the green image?
options:
a 90° rotation about point c followed by a translation 3 units left and 2 units down
a reflection in the x -axis followed by a translation 2 units right and 1 unit down
a 180° rotation about the origin followed by a translation 5 units left and 1 unit down
a reflection in the y -axis followed by a translation 4 units left and 3 units down

Explanation:

Step1: Identify coordinates of blue triangle

Blue triangle vertices: A(-5,2), B(-5,1), C(-2,1)

Step2: Test reflection over x-axis

Reflection rule: (x,y)→(x,-y). Results: A'(-5,-2), B'(-5,-1), C'(-2,-1)

Step3: Apply translation (2 right,1 down)

Translation rule: (x+2,y-1). Results: A''(-3,-3), B''(-3,-2), C''(0,-2) → matches green triangle vertices.

Step4: Verify other options fail

Other options do not produce the green triangle coordinates.

Answer:

a reflection in the x-axis followed by a translation 2 units right and 1 unit down