Question

1. the figures show the pre - image (abcd) and image (abcd) under a transformation. determine which transformation appears to be rigid.
2. triangle abc maps onto triangle abc from a single rigid motion such that

· aa || bb and bb || cc, and
· aa = bb and bb = cc.
which rigid motion maps triangle abc onto triangle abc?
a) a reflection over bb
c) a reflection over ac
b) a translation of length of bb
d) a translation of length of ac

1. a triangle and the line y = 2x are shown to the right. which grid shows the triangle reflected over the line y = 2x?

Explanation:

13.

Step1: Recall rigid - transformation properties

Rigid transformations preserve side - lengths and angles.

Step2: Analyze each option

In option A, the shape has changed its orientation and side - lengths seem to be different. In option B, the pre - image and image have the same shape and size, and the transformation appears to be a rotation. In option C, the side - lengths and angles are not preserved.

Step1: Recall properties of rigid motions

A translation is a rigid motion where every point of the pre - image is moved the same distance and in the same direction. Given that $\overrightarrow{AA'}\parallel\overrightarrow{BB'}\parallel\overrightarrow{CC'}$ and $AA' = BB'=CC'$, this indicates a translation.

Step2: Identify the length of translation

The length of the translation is the distance between corresponding points, which is the length of $BB'$.

Step1: Recall reflection properties

When reflecting a point $(x,y)$ over the line $y = mx + b$, we can use the formula for reflection. For reflection over the line $y=2x$, we can also use the property that the line of reflection is the perpendicular bisector of the line segment connecting a point and its image.

Step2: Analyze the options

By visual inspection and considering the properties of reflection over the line $y = 2x$ (the orientation and position of the triangle with respect to the line $y = 2x$), we can eliminate options. The correct reflection will have the triangle in a position such that the line $y = 2x$ is the perpendicular bisector of the line segments connecting corresponding vertices.

Answer:

B

14.