Question

understanding rigid transformations and their properties continued
5 figure abcde is reflected across a horizontal line to make an image, figure fghij. draw and label figure fghij.
6 figure abcde is rotated counterclockwise around the given center of rotation to make an image, figure fghij. draw and label figure fghij.
7 can a translation, a reflection, or a rotation of a figure ever result in an image with a different size or shape? explain.

Explanation:

Step1: Recall reflection properties

In a reflection across a horizontal line, each point of the original figure (ABCDE) has a corresponding point in the new figure (FGHIJ) such that the line of reflection is the perpendicular - bisector of the segment connecting the original point and its image. For example, point A will be reflected to a point F such that the distance from A to the line of reflection is equal to the distance from F to the line of reflection.

Step2: Recall rotation properties

For a counter - clockwise rotation around a given center of rotation, each point of the original figure (ABCDE) is rotated by a certain angle around the center of rotation to get the corresponding point in the new figure (FGHIJ). The distance from each point to the center of rotation remains the same before and after rotation.

Step3: Answer question about rigid transformations

Rigid transformations (translations, reflections, and rotations) preserve the size and shape of a figure. This is because they are isometric transformations. In a translation, all points of the figure are moved the same distance in the same direction. In a reflection, the pre - image and image are congruent as the figure is flipped over a line. In a rotation, the figure is turned around a point and the resulting image has the same size and shape as the original figure.

Answer:

1. To draw figure FGHIJ from reflecting ABCDE across a horizontal line: Measure the vertical distance of each point (A, B, C, D, E) from the line of reflection. Then, mark a point on the opposite side of the line of reflection at the same vertical distance and label it accordingly (F for A's image, G for B's image, etc.).
2. To draw figure FGHIJ from rotating ABCDE counter - clockwise around the given center of rotation: Use a protractor to measure the counter - clockwise angle of rotation for each point around the center of rotation. Keep the distance from each point to the center of rotation the same and mark the new points and label them (F, G, H, I, J).
3. No, a translation, a reflection, or a rotation of a figure will never result in an image with a different size or shape. These are rigid transformations that preserve congruence, meaning the pre - image and the image are always congruent in terms of size and shape.