Question

use the graphs below to answer questions 1 - 4.

1. describe the transformation represented on hannahs graph.
2. for giovannis graph, write a \1\ and a \2\ next to the 1st and 2nd transformations in the sequence of transformations represented by his graph. not all choices will be used.

a. reflection over x - axis
b. translation 4 units right
c. rotation 180° clockwise
d. rotation 90° clockwise
e. translation 4 units left

1. which graph(s) represent a pre - image that is congruent to the image, and which graph(s) represent a pre - image that is similar to the image?

Explanation:

Step1: Analyze the transformation in question 1

For the first graph transformation from $\triangle ABC$ to $\triangle A'B'C'$, we observe that the orientation of the triangle has changed in a mirror - like fashion across a vertical line. This is a reflection.

Step2: Analyze the transformation in question 2

For Giovanni's graph, we need to identify the two transformations. If we consider the first transformation as moving the shape horizontally and the second as changing its orientation, a translation (moving 4 units right) and a rotation (180° clockwise) can be used.

Step3: Analyze question 4

Similar figures have the same shape but not necessarily the same size. Transformations that preserve shape are translations, rotations and reflections. A translation 4 units left (option e), a 90° clock - wise rotation (option d), a 180° clock - wise rotation (option c), a translation 4 units right (option b) and a reflection over the x - axis (option a) all result in similar figures.

Answer:

1. Reflection over a vertical line.
2. a. Translation 4 units right, c. Rotation 180° clockwise
3. a. Reflection over x - axis, b. Translation 4 units right, c. Rotation 180° clockwise, d. Rotation 90° clockwise, e. Translation 4 units left