Question

question #5 g.gsr.3.3 select the notation that maps △abc onto △def. a. rotation 90° about the point a b. translation of (x + 2,y - 6) c. reflection across the line y = x d. rotation of 180° about the origin question #4 g.gsr.3.3 identify the transformation that maps △abc and △abc.

Explanation:

Step1: Analyze translation

Translation (x + 2,y - 6) would just shift the figure, not flip or rotate it to match the orientation in the image. So option b is incorrect.

Step2: Analyze reflection

Reflection across y = x would swap the x - and y - coordinates of each point. The orientation of the triangle in the image does not match what would result from a reflection across y = x. So option c is incorrect.

Step3: Analyze rotation about point A

A 90 - degree rotation about point A would not result in the orientation of the new triangle as shown. So option a is incorrect.

Step4: Analyze 180 - degree rotation about origin

A 180 - degree rotation about the origin changes the sign of both the x - and y - coordinates of each point. This results in a figure that is upside - down and flipped horizontally, which matches the transformation from △ABC to △A'B'C'. So option d is correct.

Answer:

d. Rotation of 180° about the origin