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_{x = - 1} followed by r_{y = 7} the single transformation described by (x,y)→(x,y + 12) the composite transformation described by r_{x = 1} followed by r_{x = 7} the single translation described by (x,y)→(x,y - 12)

Explanation:

Step1: Analyze translation

Check the vertical - shift. The $y$ - coordinates of the vertices of $\triangle LOW$ are shifted up by 12 units to get the vertices of $\triangle L''O''W''$. A single translation $(x,y)\to(x,y + 12)$ will map $\triangle LOW$ to $\triangle L''O''W''$.

Step2: Analyze reflection composition

Reflect $\triangle LOW$ over $x=- 1$ and then over $x = 7$. First, reflecting a point $(x,y)$ over the line $x = a$ gives the point $(2a - x,y)$. Reflecting over $x=-1$ gives $( - 2 - x,y)$ and then reflecting $( - 2 - x,y)$ over $x = 7$ gives $2\times7-(-2 - x),y=(14 + 2+x,y)=(x + 16,y)$. Also, considering the vertical position, we can analyze the transformation of the triangle's position. The composition of reflections $r_{x=-1}$ followed by $r_{x = 7}$ can also map $\triangle LOW$ to $\triangle L''O''W''$.

Answer:

• the single transformation described by $(x,y)\to(x,y + 12)$
• the composite transformation described by $r_{x=-1}$ followed by $r_{x = 7}$