Question

each parking - space in the figure can be the image of another parking - space as a glide reflection. what is the rule that maps parking space a to parking space b? the glide reflection rule is (t₍₎ o r_l)(a)=b, where l is the line with the equation

Explanation:

Step1: Identify the translation

First, count the number of units of horizontal and vertical translation. By observing the grid, we can see that to get from parking - space A to parking - space B, we move 8 units to the right and 4 units up. So the translation part of the glide - reflection is $T_{(8,4)}$.

Step2: Identify the line of reflection

The line of reflection is the horizontal line that is halfway between parking - space A and parking - space B. The y - coordinate of the mid - line between the two parking spaces is $y = 7$. So the line of reflection is $y = 7$.

Answer:

$(T_{(8,4)}\circ r_{y = 7})(A)=B$