Question

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 ( 90^{circ} ) clockwise rotation about the origin followed by a translation of

Explanation:

Step1: Analyze the rotation

When a point \((x,y)\) is rotated \(90^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(y, -x)\).

Step2: Analyze the translation

After rotation, we need to check the horizontal and vertical shift.
Let's assume a vertex of figure 1. Suppose a vertex of figure 1 is \((6,2)\). After \(90^{\circ}\) clockwise rotation about the origin, it becomes \((2,-6)\). To get to the corresponding vertex of figure 2 (say, if we consider the general position - after rotation, we observe that we need to move 7 units to the left (since \(2-7=-5\) in the x - direction) and 3 units up (since \(-6 + 3=-3\) in the y - direction, but more accurately, if we consider the overall movement of the figure).

Answer:

\(7\) units left and \(3\) units up.