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 drop - down menu with options: 90° counter clockwise, 180° clockwise, 90° clockwise rotation about the origin followed by a translation of drop - down menu.

Explanation:

Step1: Identify rotation type

Take a vertex of Figure 1, e.g., $(5,2)$. A $90^\circ$ clockwise rotation about the origin uses the rule $(x,y)\to(y,-x)$. Applying this: $(5,2)\to(2,-5)$.

Step2: Find translation values

The corresponding vertex in Figure 2 is $(-4,2)$. Calculate the horizontal translation: $-4 - 2 = -6$. Calculate the vertical translation: $2 - (-5) = 7$. So the translation is $\langle -6, 7
angle$ (6 units left, 7 units up).

Step3: Verify with other vertices

Take vertex $(8,5)$ of Figure 1: $90^\circ$ clockwise rotation gives $(5,-8)$. Apply translation: $5-6=-1$, $-8+7=-1$. The corresponding vertex in Figure 2 is $(-1,-1)$, which matches.

Answer:

$90^\circ$ clockwise rotation about the origin followed by a translation of 6 units left and 7 units up (or $\langle -6, 7
angle$)