Question

1. lines k and m are perpendicular and intersect at point r. points q and q both lie on line k such that qr = rq. which statement must be true? a) a reflection over line k maps point q onto q. b) a reflection over line m maps point q onto q. c) a translation of length qr maps point q onto q. d) a translation of length 4qr maps point q onto q. 6. which transformations will always produce congruent figures? a) dilation b) transformation c) rigid motions d) non - rigid motions 7. specify a sequence of transformations that will map abcd to pqrs. a) reflection and rotation b) rotation and translation c) reflection and translation d) rotation and dilation 8. congruent quadrilaterals jklm and pqrs are shown. which sequence of transformations maps jklm onto pqrs? a) a reflection over the x - axis followed by a translation 2 units to the right b) a reflection over the y - axis followed by a translation 8 units down and 5 units left c) a rotation 180° clockwise about the origin followed by a reflection over the y - axis d) a rotation 90° clockwise about point m followed by a translation 8 units down and 3 units left 9. points m and m are two distinct points that lie on a circle a. which statement must be true? a) point m can be reflected over am to map onto point m. b) point m can be rotated about point a to map onto point m. c) point m can be translated to a distance of am to map onto point m. d) point m can be dilated by a scale factor of am centered at point a to map onto point m.

Explanation:

5.

Step1: Recall reflection property

A reflection over a line is a transformation that maps a point to its image such that the line is the perpendicular - bisector of the segment joining the point and its image. Given that $QR = RQ'$ and $Q$ and $Q'$ lie on line $k$, a reflection over line $k$ maps point $Q$ onto $Q'$.

Step1: Understand transformation types

Rigid motions (translations, rotations, and reflections) preserve the size and shape of a figure, which means they produce congruent figures. Dilations change the size of a figure, and non - rigid motions are not well - defined in the context of producing congruent figures. Transformations in general include dilations which do not always produce congruent figures.

Step1: Analyze the orientation and position

The orientation of $ABCD$ and $PQRS$ is different, which may require a rotation. Also, the position of the figures is different, which requires a translation. A dilation would change the size of the figure, and we can see that the size of $ABCD$ and $PQRS$ is the same. A reflection alone may not be sufficient to map the figure.

Answer:

A. A reflection over line k maps point Q onto Q'

6.