Question

which of the following transformations maps △low to △low? select two correct answers. (1 point) the single transformation described by (r_{270}) the composite transformation described by (r_{y - 1}) followed by (r_{y+7}) the single transformation described by ((x,y)\to(x,y + 12)) the single transformation described by ((x,y)\to(x,y - 12)) the composite transformation described by (r_{y - 1}) followed by (r_{x - 3})

Explanation:

Step1: Analyze vertical - shift

We can observe that $\triangle LOW$ is shifted upwards to get $\triangle L'O'W'$. If we consider a point $(x,y)$ in $\triangle LOW$ and its corresponding point $(x,y')$ in $\triangle L'O'W'$, the $x$ - coordinate remains the same and the $y$ - coordinate changes by a positive value. The transformation $(x,y)\to(x,y + 12)$ represents a vertical upward shift of 12 units, which can map $\triangle LOW$ to $\triangle L'O'W'$.

Step2: Analyze composite reflection

If we first reflect $\triangle LOW$ over the $y$ - axis and then reflect the resulting triangle again over the $y$ - axis, the net result is equivalent to a translation in some cases. In this situation, two consecutive reflections over the $y$ - axis for $\triangle LOW$ can also map it to $\triangle L'O'W'$ as the orientation and position can be made to match through this composite transformation.

Answer:

• The single transformation described by $(x,y)\to(x,y + 12)$
• The composite transformation described by $r_{y - axis}$ followed by $r_{y - axis}$