Question

select the correct answer from each drop - down menu.
consider figures 1 and 2 on the coordinate plane.
which sequence of transformations maps figure 1 onto figure 2?
figure 1 is mapped onto figure 2 by a 180° clockwise rotation about the origin followed by a translation of

Explanation:

Step1: Analyze the rotation

A \(180^{\circ}\) clockwise rotation about the origin \((x,y)\to(-x, -y)\). After rotation, we need to check the translation.

Step2: Analyze the translation

After rotation, we observe the horizontal movement. The \(x -\)coordinate change: from positive \(x\) (for figure 1) to negative \(x\) (after rotation) and then to more negative \(x\) (figure 2). The number of units of horizontal shift: If we assume a point \((6,3)\) on figure 1. After \(180^{\circ}\) rotation, it becomes \((- 6,-3)\). To get to figure 2 (say a corresponding point \((-13,-3)\) shifted from \((-6,-3)\)), we move \(7\) units to the left (since \(-6-7=-13\)).

Answer:

\(180^{\circ}\) clock - wise rotation about the origin followed by a translation of \(7\) units left.