Question

1. which the following lists the correct order of transformations that occurred in the image below? a reflection over the y - axis followed by a reflection over the x - axis. a translation followed by a reflection over the x - axis. a reflection over the y - axis followed by a translation. a 180° rotation followed by a translation.

Explanation:

Step1: Analyze the first - step transformation

The green triangle $\triangle ABC$ is reflected over the $y$-axis to get the blue triangle $\triangle A'B'C'$. When a point $(x,y)$ is reflected over the $y$-axis, its new coordinates become $(-x,y)$.

Step2: Analyze the second - step transformation

The blue triangle $\triangle A'B'C'$ is then reflected over the $x$-axis to get the red triangle $\triangle A''B''C''$. When a point $(x,y)$ is reflected over the $x$-axis, its new coordinates become $(x, - y)$.

Answer:

A reflection over the y - axis followed by a reflection over the x - axis.