Unit 1 Transformations with Rigid Motions Review

Which of the following transformations to ∆ABC would NOT preserve size and shape?

• rotation 270° clockwise

• translation of (x – 7, y + 4)

• reflection over the x-axis

• dilation of scale factor 3

The vertices of ∆ABC are A(2, 1), B(3, 4), and C(1, 3). If ∆ABC is translated 3 unit down and 2 units to the left to create ∆DEF, what are the coordinates of the vertices of ∆DEF?

• D(0, –1), E(0, 3), F(–2, –2)

• D(–2, –2), E(0, 3), F(–1, 0)

• D(0, -2), E(1, 1), F(-1, 0)

• D(–1, 0), E(0, 3), F(–2, 2)

Which of the following statements about rigid transformations is FALSE?

• In a translation, the segments joining points of the pre-image and their images are parallel.

• In a reflection, the segments joining points of the pre-image and their images are parallel to the line of reflection.

• In a reflection, the points of the pre-image are always the same distance away from the line of reflection as the corresponding points of the image.

• In a rotation, the points of the pre-image are always the same distance away from the center of rotation as the corresponding points of the image.

• rotation

• translation

• reflection

• not enough information to determine

What will be the coordinates of point A if figure ABCD is reflected across the y-axis?

• (2, -5)

• (2, 5)

• (-5, 2)

• (5, 2)

Which of the following graphs is the result of a reflection of ∆PQR?

• 
• 
• 
• 

Which of the following transformations or combinations of transformations can help Delia prove her conjecture? Explain how the statements you select help Delia prove her conjecture.

Select all that apply.

• Rotate figure I 180° around point P.

• Rotate figure I 90° clockwise around point P, and then reflect the image across line n.

• Reflect figure I across line m, and then reflect the image across line n.

• Reflect figure I across line n, and then rotate the image 90° counterclockwise around point P.

• Reflect figure I across line s.

Which transformation can be used to map Figure 1 onto itself and can also be used to map Figure 2 onto itself?

• A reflection over a line through the center of the figure that is parallel to one of the sides of the figure.

• A rotation of 180° about the center of the figure.

• A rotation of 90° clockwise about the center of the figure.

• A reflection over one of the diagonals of the figure.

The figure shows two perpendicular lines s and r, intersecting at point P in the interior of a trapezoid. Line r is parallel to the bases and bisects both legs of the trapezoid. Line s bisects both bases of the trapezoid.

Determine which transformation will ALWAYS carry the figure onto itself?

• a rotation of 90° clockwise about point P

• a rotation of 180° clockwise about point P

• a reflection across line r

• a reflection across line s

The rectangle is rotated 90º counterclockwise about the origin. Which of the following ordered pairs is a vertex of the rectangle’s image?

• (–5, 1)

• (–4, –1)

• (4, –5)

• (4, 4)