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〈〉∘r_t)(a)=b, where t is the line with the equation □.

Explanation:

Step1: Identify the mid - point between A and B

The mid - point between the centers of parking space A and B in the x - direction is at \(x = 7\). The line of reflection \(t\) for the glide - reflection is the vertical line passing through this mid - point. The equation of a vertical line is of the form \(x = a\), where \(a\) is the x - coordinate of any point on the line. So the equation of the line \(t\) is \(x=7\).

Step2: Determine the translation part

The translation part of the glide - reflection moves the reflected point (after reflection across \(x = 7\)) to the final point. Observing the y - coordinates of corresponding points of A and B, we can see that there is no vertical translation. In the x - direction, if we reflect a point across \(x = 7\) and then translate, we note that the glide - reflection can be described as a translation along the line \(x = 7\). The translation vector \(\vec{v}\) for the glide - reflection from A to B (after reflection) has a horizontal component. The distance between the centers of A and B in the x - direction is \(4\) units. The translation vector for the glide - reflection is \(\langle4,0
angle\).

Answer:

\((T_{\langle4,0
angle}\circ r_{x = 7})(A)=B\)