Question

the figure shown below is rotated 90° clockwise about the point (0, -1) and then reflected across the y - axis in order to create figure x₁y₁z₁. what is the length of \\( \overline{x_1z_1} \\) after the transformations are completed?

Explanation:

Step1: Recall transformation properties

Rotations and reflections are rigid transformations. Rigid transformations preserve the lengths of segments.

Step2: Find the length of \( XZ \)

From the graph, the coordinates of \( X(-5,-1) \) and \( Z(-1,-1) \). Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \), since \( y_1=y_2=-1 \), \( d=\vert x_2 - x_1\vert=\vert-1-(-5)\vert=\vert-1 + 5\vert = 4 \)

Answer:

\( 4 \)