Question

making predictions with transformations
which of the following transformations maps △low to △low? select two correct answers.
(1 point)
□ 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 single transformation described by (r_{270})
□ the composite transformation described by (r_{x = 1}) followed by (r_{x = 7})

Explanation:

Step1: Analyze vertical - shift transformation

A transformation of the form $(x,y)\to(x,y - 12)$ represents a vertical shift downwards by 12 units. If the transformation from $\triangle LOW$ to $\triangle L''O''W''$ is a vertical shift, we need to check the vertical distance between corresponding points.

Step2: Analyze composite reflection transformation

A composite transformation of two reflections $r_{y = 1}$ followed by $r_{y=7}$ can also map a triangle to a new position. When we reflect a point across two parallel lines $y = a$ and $y = b$, the net - effect is a translation perpendicular to the lines of reflection. The distance of the translation is $2|b - a|$. Here, $a = 1$ and $b = 7$, so the distance of the translation is $2|7 - 1|=12$ units in the vertical direction.

Answer:

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