Question

100 points QUICK!

Which transformation changes triangle ABC to triangle A'B'C'?

A coordinate grid is labeled from negative 6 to 0 to 6 on both axes. Triangle ABC is drawn in the fourth quadrant. Point A is the ordered pair 2, negative 4, point B is the ordered pair 5, negative 1, point C is the ordered pair 4, negative 5. Triangle A prime, B prime, C prime is drawn in the second quadrant. Point A prime is the ordered pair negative 2, 4, point B prime is the ordered pair negative 5, 1, point C prime is the ordered pair negative 4, 5.

Reflection about the y-axis followed by translation up by 8 units
Reflection about the x-axis followed by translation left by 4 units
Rotation 90 degrees clockwise about the origin
Rotation 180 degrees counterclockwise about the origin

Answer 1

A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin

Explanation:

Answer 2

"A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin"

Explanation:

since the choices all have rotation about the origin, we must shift the original triangle in a suitable position. This is done by connecting any of the points of A'B'C' to the origin, and extend this line segment, as shown in the picture.

The most appropriate point is C', and we draw C" such that C'O=OC", and C', O and C" are collinear.

We see that the distance CC'' is 5.

So

Answer is:

"A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin"