Question

1. arya is a computer graphics designer and is working on an ad for the local coffee shop. the figure shows a coffee mug in two different positions. which describes the transformation of the coffee mug in position i to the image in position ii? a) translation down and a reflection over a vertical line. b) a reflection over a horizontal line and a translation down. c) 180° rotation. d) translation to the right and a reflection over a vertical line. 17. which figure represents a reflection of figure 3? a) figure 2 c) figure 5 b) figure 4 d) figure 1 18. a parallelogram has vertices at (0, 0), (0, 6), (4, 4), and (4, -2). which transformation maps the parallelogram to itself? a) a reflection across the line x = 2. b) a rotation of 180° about the point (0, 0). c) a reflection across the line y = 2. d) a rotation of 180° about the point (2, 2).

Explanation:

Step1: Analyze question 16

Observe the position change of the coffee - mug. A $180^{\circ}$ rotation changes the orientation and position in a way that matches the transformation from position I to position II. A translation and reflection combination in options A, B, and D do not match the given transformation.

Step2: Analyze question 17

For a reflection, the figure should be flipped over a line. By visual inspection, figure 4 is the reflection of figure 3 over a vertical line.

Step3: Analyze question 18

For a parallelogram with vertices $(0,0),(0,6),(4,4),(4, - 2)$, the mid - point of the line segment connecting $(0,0)$ and $(4,4)$ and the mid - point of the line segment connecting $(0,6)$ and $(4,-2)$ is $(2,2)$. A $180^{\circ}$ rotation about the point $(2,2)$ maps the parallelogram to itself.

Answer:

1. C. $180^{\circ}$ rotation.
2. B. figure 4
3. D. A rotation of $180^{\circ}$ about the point $(2,2)$.