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.

vocabulary
transformation a change in position or size of a figure.
translation a transformation that moves each point of a figure the same distance and in the same direction.

Explanation:

Step1: Analyze the translation

The original figure is moved right 6 units and up 3 units (counting grid spaces from each vertex of the original gray figure to the corresponding vertex of the green image figure).

Step2: Describe reflection drawing process

For the reflection:

1. Identify each vertex of the given trapezoid.
2. Measure the perpendicular distance from each vertex to the implicit vertical reflection line (assumed to be a vertical grid line, e.g., $x=7$ for the given grid).
3. Plot each reflected vertex on the opposite side of the line, at the same perpendicular distance.
4. Connect the reflected vertices to form the reflected image.

Answer:

1. The original figure was translated 6 units to the right and 3 units up to create the image.
2. (Reflected figure description): The reflected image is a mirror copy of the given trapezoid across the vertical line of reflection, with each vertex equidistant from the line on the opposite side of the original figure. When drawn, it will be symmetric to the original trapezoid with respect to the reflection line.