Question

1. describe the sequence of transformations that will carry nopqfg onto nopqfg. a. rotation, reflection b. translation, rotation c. translation, reflection d. reflection, rotation 4. which of the following best describes the transformation shown above? a. translation b. reflection c. rotation d. none of the above 5. describe the sequence of transformations that will carry △abc onto △abc. a. reflection, rotation b. translation, rotation c. reflection, translation d. rotation, translation 6. which transformation will map the figure onto itself? a. rotation 180° about the origin b. reflection across the y - axis c. rotation 90° clockwise about the origin d. reflection across the x - axis 7. which transformation will map the figure onto itself? choose all that apply. a. rotation 90° clockwise about the origin b. reflection across the line y = x c. rotation 180° clockwise about the origin d. reflection across the x - axis

Explanation:

Step1: Analyze first problem

Observe the orientation and position change of NOPQFG to N'O'P'Q'F'G'. First, it seems to be translated (moved) and then reflected. So the answer for the first problem is C. translation, reflection.

Step2: Analyze second problem

The figure of FGH to F'G'H' shows a reflection over a vertical - like line. So the answer for the second problem is B. Reflection.

Step3: Analyze third problem

For △ABC to △A'B'C', first, it is reflected and then translated. So the answer for the third problem is C. reflection, translation.

Step4: Analyze fourth problem

For the trapezoid, a 180° rotation about the origin will map it onto itself as the shape has rotational symmetry of order 2 about the origin. So the answer for the fourth problem is A. rotation 180° about the origin.

Step5: Analyze fifth problem

For a circle, a 90° clock - wise rotation about the origin, a 180° clock - wise rotation about the origin, a reflection across the line y = x, and a reflection across the x - axis will all map it onto itself as a circle has infinite lines of symmetry and rotational symmetries. So the answers for the fifth problem are A. rotation 90° clockwise about the origin, B. reflection across the line y = x, C. rotation 180° clockwise about the origin, D. reflection across the x - axis.

Answer:

1. C. translation, reflection
2. B. Reflection
3. C. reflection, translation
4. A. rotation 180° about the origin
5. A. rotation 90° clockwise about the origin, B. reflection across the line y = x, C. rotation 180° clockwise about the origin, D. reflection across the x - axis