Question

sharon uses a sequence of transformations with figure abcd to create figure efgh. complete the sentence about the sequence of transformations that maps figure abcd to figure efgh. enter your answers in the boxes. a rotation of \\(\square\\) degrees counterclockwise about the origin followed by a reflection across the line \\(x = \square\\) maps figure abcd onto figure efgh.

Explanation:

Step1: Analyze Rotation Angle

First, observe the orientation of Figure ABCD and EFGH. A 90 - degree counter - clockwise rotation about the origin will change the coordinates in a way that (x,y)→(-y,x). Let's check the key points. For example, if we take a point from ABCD, after a 90 - degree counter - clockwise rotation, and then a reflection, we can get to EFGH. So the rotation angle is 90 degrees.

Step2: Analyze Reflection Line

After a 90 - degree counter - clockwise rotation, we need to reflect across a vertical line \(x = k\) to map ABCD to EFGH. Let's consider the center of the figures. The mid - point or the symmetry after rotation and reflection. The line \(x = 2\) (we can calculate by looking at the horizontal shift needed. After rotation, the reflection across \(x = 2\) will align the figures. So the line of reflection is \(x=2\).

Answer:

The rotation angle is 90 degrees and the line of reflection is \(x = 2\). So the answers are 90 and 2.