Geometry Transformations

Polygon KLMNP is reflected across the line x = −1. What are the coordinates of the image of vertex P after this reflection?

Answer explanation

Construct the vertical line x = -1, then flip the point P over that and name the new coordinates of P' .

Polygon KLMNP is rotated by 180° counterclockwise about the origin. What are the coordinates of the image of vertex L after this rotation?

Answer explanation

Consult your notes for rules of rotations about the origin.

Which sequence of transformations maps triangle DEF to congruent triangle ABC

• Translate point E, 9 units left , then translate E , 4 units up.

• Rotate about point D, 90 degrees CW , then translate 3 units up

• Rotate triangle DEF about point F, 180 degrees.

• Rotate clockwise 90 degrees about point E, then translate up 10 units.

Answer explanation

Sketch the shapes on scrap paper and perform each sequence of transformations to see which maps DEF onto triangle ABC.

Which sequence of transformations maps quadrilateral WXYZ to ABCD?

• Sequence B

• Sequence A

• Both sequence A & B

• Neither sequence A or B

Determine the line of reflection that maps triangle AB to triangle A'B'C'.

Answer explanation

Sketch the shapes on scrap paper, fold along the line that results in the pre-image landing on the image. Name the fold line.

Which transformation would NOT map the rectangle onto itself?

• a reflection over the x axis

• a reflection over the line x= 4

• a rotation of 180 degrees about the origin

• a rotation of 180 degrees about the point ( 4, 0 )

Answer explanation

Try each suggested transformation and see which DOES NOT work.

If the regular pentagon is rotated clockwise about its center, what minimum number of degrees are needed in the rotation to carry the shape onto itself?

Answer explanation

Hint: a circle has 360 degrees. Divide that by the number of sides to determine the interior angles. 

Rotate the triangle ABC, 90 degrees about the point (2,1) . What are the new coordinates for C' ?

Answer explanation

First label point C. Next subtract the point of rotation. Then, use rotation rules for rotation about the origin. Lastly, add back in the point of rotation coordinates.

Triangle ABC with vertices A(6, 9), B(8, 5), and C(5, 2) is mapped onto triangle A'B'C' with vertices A'(−3, −2), B'(−1, −6), and C'(−4, −9). Which vector is used in the translation?

Answer explanation

Think how can I get from one vertex pre-image to that vertex's image.

Which of the following statements is true about the given design?

• There are multiple lines of symmetry in the design.

• The design's angle of rotational symmetry is 90°

• The design's angle of rotational symmetry is 180°

• The design is symmetrical about a vertical line through its center.

Answer explanation

Try drawing lines of symmetry, will the small outside bubbles land on each other? How many degrees must you rotate the shape for it to land on itself?