Question

lesson 1.2 understanding rigid transformations w5
example
figure q is a transformation of figure p. compare
the figures. tell what is the same and what is
different about figure p and figure q. identify
the transformation.
same: the figures have the same shape and size. parallel sides
in figure p correspond to parallel sides in figure q. the lengths
of corresponding sides are the same, and the measures of
corresponding angles are the same.
different: figure q is in a different location than figure p and
facing a different direction. figure q is a mirror image of figure p.
the transformation is a reflection.

1. figure a was transformed to form figures b, c, and d.

a. which figure is a translation of figure a?
draw an arrow to show the direction of the translation.

b. which figure is a reflection of figure a?
draw the line of reflection.

c. which figure is a rotation of figure a?
draw the center of rotation.

Explanation:

Part (a)

Step1: Recall Translation Definition

A translation is a rigid transformation that slides a figure without changing its shape, size, or orientation. So we check which figure (B, C, D) has the same shape, size, and orientation as A.

Step2: Compare Figures

• Figure D: Has the same shape, size, and orientation as A. The direction of translation is likely down (from A's position to D's position, same horizontal alignment, vertical shift down).
• Figure B: Different orientation (the triangular part is on the left, A's is on the right).
• Figure C: Different orientation (triangular part is reversed and at the bottom - left).

Step1: Recall Reflection Definition

A reflection is a rigid transformation that flips a figure over a line (line of reflection), creating a mirror image. The shape and size remain the same, but orientation (left - right or top - bottom) flips.

Step2: Compare Figures

• Figure B: When we imagine a vertical line of reflection (maybe through the middle of the horizontal distance between A and B), the shape is a mirror image. The triangular part of A (on the right) is on the left in B, and the rest of the rectangle is mirrored.
• Figure C: Orientation is rotated, not reflected.
• Figure D: Orientation is same (translation), not reflected.

Step1: Recall Rotation Definition

A rotation is a rigid transformation that turns a figure around a fixed point (center of rotation) by an angle. The shape and size remain the same, but the figure is rotated.

Step2: Compare Figures

• Figure C: The triangular part of A (on the right, pointing up) is on the left - bottom, pointing down, which suggests a rotation (e.g., 180 - degree rotation or some angle). The center of rotation would be a point (maybe the center of the "rectangular - triangular" combined shape or a grid - intersection point) around which A is rotated to get C.
• Figure B: Reflection, not rotation.
• Figure D: Translation, not rotation.

Answer:

a. Figure D is a translation of figure A. The arrow should be drawn vertically downward from figure A to figure D (or along the grid to show the slide direction, e.g., 0 horizontal units and some vertical units down).

Part (b)