Question

name: section date: transformations common core geometry classwork measurement and construction for each of the following transformations on image a, resulting in image b, label it as a rotation, a reflection, a translation, or a dilation. 1. a b a b 2. a b a b 3. a b a b 4. a b a b 5. which of the transformations above preserved the size and shape of the original image? use tracing paper if you need to check. 6. one of the transformations above was a dilation by a scale factor of k. the scale factor is the multiplicative amount that the picture has been enlarged. to calculate it, divide any length on b by the corresponding length on a. use your ruler to make these measurements and then calculate the scale factor of the dilation. round to the nearest tenth. common core geometry, unit #2 - transformations, rigid motions, and congruence - lesson #1 emathinstruction, red hook, ny 12571, © 2017

Explanation:

Step1: Analyze transformation in 1

The image of the horse in B is a mirror - image of A across a vertical line. So it is a reflection.

Step2: Analyze transformation in 2

The 'Art' in B is the same as in A but in a different position. It is a translation.

Step3: Analyze transformation in 3

The cyclist in B is rotated around a point compared to A. It is a rotation.

Step4: Analyze transformation in 4

The penguin in B is larger than in A. It is a dilation.

Step5: Identify size - and shape - preserving transformations

Rotations, reflections, and translations (rigid motions) preserve size and shape. So the transformations in 1, 2, and 3 preserve size and shape.

Step6: Calculate scale factor (no actual measurements given here, just the concept)

For a dilation, if we measure a length \(l_A\) on A and the corresponding length \(l_B\) on B, the scale factor \(k=\frac{l_B}{l_A}\).

Answer:

1. Reflection
2. Translation
3. Rotation
4. Dilation
5. 1, 2, 3
6. (No numerical answer as no measurements provided. Concept: \(k = \frac{\text{length on B}}{\text{length on A}}\))