Question

The figure shows two similar triangles on a coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 3, 3, vertex B on ordered pair 0, 0 and vertex C on ordered pair negative 6, negative 3. A triangle A prime B prime C prime is also shown with vertex A prime on ordered pair 1, 1, vertex B prime on ordered pair 0, 0, and vertex C prime on ordered pair 2, negative 1. Which set of transformations have been performed on triangle ABC to form triangle A'B'C'? Dilation by a scale factor of 1 over 3 followed by reflection about the x-axis Dilation by a scale factor of 3 followed by reflection about the x-axis Dilation by a scale factor of 1 over 3 followed by reflection about the y-axis Dilation by a scale factor of 3 followed by reflection about the y-axis

Answer 1

From what I know, figure ABC has gotten smaller so you wouldn't use either options that suggests a dilation of 3, because that would mean it got bigger. (But please correct me if I'm wrong.) Also, if you look at the little unit square measurements on the graph, looking at figure ABC, C is 6 units from B, while in figure A'B'C', C' is 2 units from B', which 6÷2=3 meaning that A'B'C' would most likely be a third of its size.

Next the figure is being mirrored over the y-axis which is the vertical line going up and down.

So the answer would be the option that says

"Dilation by a scale factor of 1 over 3 followed by a reflection about the y-axis"

I hope that it's right, because I haven't practiced this in a while, and I hope this made some sense.