Similarity With All Transformations

1) A rotation of 180° about the origin sends (3, –4) to:

(–3, 4)

(3, 4)

(–3, –4)

(4, –3)

A 180° rotation about the origin sends (x, y) → (–x, –y).

Explanation

A 180° rotation about the origin sends (x, y) → (–x, –y).

2) Which is NOT a similarity transformation?

Translation

Rotation

Reflection

Shear

Shears change angles, so they are not similarity transformations.

Explanation

Shears change angles, so they are not similarity transformations.

3) Which transformation produces a mirror image across a line?

Translation

Reflection

Rotation

Dilation

Reflections create mirror images across a line.

Explanation

Reflections create mirror images across a line.

4) Which statement is true about translations?

They move figures without rotating or resizing

They resize figures

They flip figures

They distort angles

Translations slide figures only.

Explanation

Translations slide figures only.

5) A triangle with angles 40°, 60°, and 80° is dilated to create a larger similar triangle. Which property remains unchanged after the transformation?

Side lengths

Angle measures

Perimeter

Area

Dilations keep angles the same; lengths and perimeter scale.

Explanation

Dilations keep angles the same; lengths and perimeter scale.

6) A triangle has coordinates (0,0), (1,2), (3,1). After dilation with scale factor 2, the new coordinates are:

(0,0), (2,4), (6,2)

(0,0), (1,1), (2,2)

(0,0), (3,6), (9,3)

(0,0), (2,3), (5,1)

Scale factor 2 multiplies each coordinate by 2.

Explanation

Scale factor 2 multiplies each coordinate by 2.

7) Which transformation best demonstrates congruence by a slide (no turn or flip)?

Dilation

Rotation

Translation

Reflection

A translation is a slide with no turn or flip, and it preserves congruence.

Explanation

A translation is a slide with no turn or flip, and it preserves congruence.

8) A rectangle is dilated by a factor of 3. Which is true?

Angles stay the same

Angles triple

Sides stay the same

Shape distorts

Dilations preserve angle measures; side lengths scale.

Explanation

Dilations preserve angle measures; side lengths scale.

9) If a figure is rotated 360°, the image is:

Enlarged

Reduced

Congruent

Reversed

A 360° rotation returns the figure to its original position.

Explanation

A 360° rotation returns the figure to its original position.

10) Which is the correct definition of similar figures?

Figures with the same area

Figures with proportional sides and equal angles

Figures that overlap

Figures that are congruent

That is the definition of similar figures.

Explanation

That is the definition of similar figures.

11) A reflection across the y-axis sends (–5, 3) to:

(5, 3)

(–5, –3)

(3, –5)

(–3, 5)

Reflect across y-axis: (x, y) → (–x, y).

Explanation

Reflect across y-axis: (x, y) → (–x, y).

12) Triangle A has vertices at (0,0), (2,0), (0,2) and Triangle B has vertices at (0,0), (4,0), (0,4). Which transformation maps Triangle A onto Triangle B?

Dilation, scale factor 2

Rotation 90°

Reflection across x-axis

Translation

Each coordinate doubles, so side lengths double.

Explanation

Each coordinate doubles, so side lengths double.

13) Which transformation can change the size of a figure?

Rotation

Reflection

Translation

Dilation

Dilations change size by a scale factor.

Explanation

Dilations change size by a scale factor.

14) Which sequence of transformations proves two rectangles are similar?

Translation then reflection

Rotation then translation

Dilation then translation

Reflection then rotation

Dilation creates proportional sides, translation repositions without changing shape.

Explanation

Dilation creates proportional sides, translation repositions without changing shape.

15) What sequence transforms a triangle into a similar triangle of different size but same orientation?

Dilation only

Reflection then rotation

Translation then reflection

Rotation only

A dilation changes size but keeps orientation if the scale factor is positive.

Explanation

A dilation changes size but keeps orientation if the scale factor is positive.

16) Point A is located at (2,3). After reflection across the x-axis, the coordinates of A are:

(–2, 3)

(2, –3)

(3, 2)

(–2, –3)

Reflect across x-axis: (x, y) → (x, –y).

Explanation

Reflect across x-axis: (x, y) → (x, –y).

17) What is the center of rotation that maps a figure onto itself at 120°?

The midpoint of one side

The centroid

The center of the figure

Any point on the plane

A figure that maps to itself by 120° has rotational symmetry about its center.

Explanation

A figure that maps to itself by 120° has rotational symmetry about its center.

18) Which transformation changes orientation but preserves distance?

Rotation

Reflection

Translation

Dilation

Reflections reverse orientation but preserve distances and angles.

Explanation

Reflections reverse orientation but preserve distances and angles.

19) Two triangles are similar if:

Their angles are equal and sides are proportional

Their sides are congruent

Their angles are congruent and sides are equal

They are congruent

That is the definition of similarity.

Explanation

That is the definition of similarity.

20) A square has vertices at (0,0), (0,2), (2,2), (2,0). A 90° counterclockwise rotation of this square about the origin places the bottom-right corner at:

(2, 0)

(–2, 0)

(0, 2)

(0, –2)

90° counterclockwise: (x, y) → (–y, x). For (2, 0), result is (0, 2).

Explanation

90° counterclockwise: (x, y) → (–y, x). For (2, 0), result is (0, 2).

Similarity with All Transformations

1) A rotation of 180° about the origin sends (3, –4) to:

2)

What first name or nickname would you like us to use?

2) Which is NOT a similarity transformation?

3) Which transformation produces a mirror image across a line?

4) Which statement is true about translations?

5) A triangle with angles 40°, 60°, and 80° is dilated to create a larger similar triangle. Which property remains unchanged after the transformation?

6) A triangle has coordinates (0,0), (1,2), (3,1). After dilation with scale factor 2, the new coordinates are:

7) Which transformation best demonstrates congruence by a slide (no turn or flip)?

8) A rectangle is dilated by a factor of 3. Which is true?

9) If a figure is rotated 360°, the image is:

10) Which is the correct definition of similar figures?

11) A reflection across the y-axis sends (–5, 3) to:

12) Triangle A has vertices at (0,0), (2,0), (0,2) and Triangle B has vertices at (0,0), (4,0), (0,4). Which transformation maps Triangle A onto Triangle B?

13) Which transformation can change the size of a figure?

14) Which sequence of transformations proves two rectangles are similar?

15) What sequence transforms a triangle into a similar triangle of different size but same orientation?

16) Point A is located at (2,3). After reflection across the x-axis, the coordinates of A are:

17) What is the center of rotation that maps a figure onto itself at 120°?

18) Which transformation changes orientation but preserves distance?

19) Two triangles are similar if:

20) A square has vertices at (0,0), (0,2), (2,2), (2,0). A 90° counterclockwise rotation of this square about the origin places the bottom-right corner at: