Question

1. the graph shows line l and line m intersect to form a 45° angle at e. kiara transforms quadrilateral abcd using the following sequence: 1. abcd is reflected over line m. 2. abcd is reflected over line l. kiara could also transform the quadrilateral in one transformation. what is a single transformation that would map quadrilateral abcd onto quadrilateral abcd? reflect quadrilateral abcd over a line that is halfway between lines l and m.

Explanation:

Step1: Recall reflection - rotation relationship

When a figure is reflected over two intersecting lines, the composition of these two reflections is equivalent to a rotation.

Step2: Determine rotation angle

The angle between the two intersecting lines \(l\) and \(m\) is \(45^{\circ}\). The angle of rotation is \(2\theta\), where \(\theta\) is the angle between the two lines of reflection. So the rotation angle is \(2\times45^{\circ}=90^{\circ}\). The center of rotation is the point of intersection of the two lines of reflection, which is point \(E\).

Answer:

Rotate quadrilateral \(ABCD\) \(90^{\circ}\) about point \(E\)