Question

determine a series of transformations that would map figure q onto figure r.
answer attempt 1 out of 2
a followed by a
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Explanation:

Step1: Analyze Rotation

First, we can rotate Figure Q 90 degrees clockwise (or counter - clockwise, but clockwise is a common choice here) about the origin. This rotation will align the orientation of Figure Q more closely to that of Figure R. The rule for a 90 - degree clockwise rotation about the origin \((x,y)\to(y, - x)\).

Step2: Analyze Translation

After the rotation, we need to translate (shift) the figure. Let's assume the center of Figure Q (or a key vertex) after rotation. We can calculate the horizontal and vertical shifts needed. Looking at the coordinates, after rotation, we can translate the figure 10 units to the right (in the x - direction) and 2 units down (in the y - direction) (the exact translation can be determined by comparing corresponding vertices of Q (after rotation) and R). Alternatively, we could first translate and then rotate, but a common sequence is rotation followed by translation. For example, rotate Figure Q 90° clockwise about the origin, then translate it 10 units right and 2 units down. Another possible sequence: reflect Figure Q over a vertical line (e.g., \(x=- 2\)) to get a mirrored image, then translate it 10 units right and 2 units down. But a more straightforward series is a rotation (90° clockwise) followed by a translation.

Answer:

One possible series of transformations: Rotate Figure Q 90° clockwise about the origin, then translate it 10 units to the right and 2 units down. (Or other valid combinations like reflection followed by translation, but rotation - translation is a common valid series here.)