Question

determine a series of transformations that would map figure u onto figure v.
answer attempt 1 out of 2
a followed by a

Explanation:

Step1: Analyze Rotation

First, we can consider rotating Figure U 180 degrees about the origin. A 180 - degree rotation about the origin \((x,y)\to(-x,-y)\) will flip the figure across both axes. This will align the orientation of Figure U more closely to Figure V.

Step2: Analyze Translation

After the 180 - degree rotation, we need to translate (move) the figure. Let's consider the horizontal and vertical shifts. Looking at the positions, after rotating 180 degrees, we can translate the figure 16 units to the right (in the x - direction) and 10 units up (in the y - direction) to map Figure U onto Figure V. Another possible series: Reflect Figure U over the x - axis (or y - axis) first, then translate. For example, reflect Figure U over the x - axis (which changes the sign of the y - coordinate \((x,y)\to(x, - y)\)), then translate 16 units right and 2 units up. But a common and simple series is: Rotate 180 degrees about the origin, then translate 16 units right and 10 units up. Or another approach: Reflect over the origin (which is equivalent to 180 - degree rotation) then translate.

Answer:

One possible series of transformations is a 180 - degree rotation about the origin followed by a translation 16 units to the right and 10 units up (or other valid combinations like reflection over x - axis, then reflection over y - axis, then translation, etc.).