Question

select the correct description for the transformation of triangle abc to triangle a b c. possible points: 7.14 reflection over the x - axis, 90° rotation reflection over the y - axis, translation (x, y + 5) 180° rotation, reflection over x - axis reflection over the y - axis, translation (x, y - 5)

Explanation:

Step1: Analyze x - coordinates

The x - coordinates of the vertices of $\triangle ABC$ change their signs in $\triangle A'B'C'$. For example, if a vertex of $\triangle ABC$ has coordinates $(x,y)$, the corresponding vertex of $\triangle A'B'C'$ has coordinates $(-x,y)$ initially. This indicates a reflection over the y - axis.

Step2: Analyze y - coordinates

After the reflection over the y - axis, we observe that the y - coordinates of the vertices of the reflected triangle are decreased by 5. For a point $(x,y)$ after reflection over the y - axis (becoming $(-x,y)$), it is further transformed to $(-x,y - 5)$. This is a translation of the form $(x,y)\to(x,y - 5)$.

Answer:

reflection over the y - axis, translation $(x,y - 5)$