Question

example: the gray figure is a transformation of the green figure. compare the figures. tell what is the same and what is different about the original figure and its image. identify the transformation. same: the figures have the same shape and size. parallel lines are still parallel and perpendicular lines are still perpendicular. the lengths of the sides are the same, and the measures of the angles are the same. different: the image is in a different location than the original figure. the transformation is a translation. 1 describe how the original figure in the example problem was moved to get the image. 2 a figure and a line of reflection are shown. draw the image of the figure after it is reflected across the line. 3 look at the image you drew in problem 2. are the properties of the sides and angles in the image the same as the properties of the sides and angles in the original figure? explain.

Explanation:

Step1: Analyze translation in problem 1

Translation involves moving a figure. By observing the grid - like background in the example, we can count the units of movement. The original figure moves 4 units to the right and 3 units down.

Step2: Draw reflection in problem 2

To draw the reflection of a figure across a line, for each point in the original figure, measure the perpendicular distance to the line of reflection. Then, mark a point on the opposite side of the line of reflection at the same perpendicular distance. Connect these new points to form the reflected image.

Step3: Analyze properties in problem 3

A reflection is a rigid transformation. Rigid transformations preserve side - lengths and angle - measures. So, the properties of the sides (lengths) and angles (measures) in the reflected image are the same as those in the original figure.

Answer:

1. The original figure moves 4 units to the right and 3 units down.
2. (Here, a visual drawing is required. Since this is text - based, the steps to draw are: for each vertex of the original figure, measure the perpendicular distance to the line of reflection. Mark a point on the opposite side of the line of reflection at the same perpendicular distance. Connect the new vertices to form the reflected figure.)
3. Yes, because reflection is a rigid transformation that preserves side - lengths and angle - measures.