Name: ______Period: ______Date: ______

Review: Transformations and Congruence

For #1-#8, name the transformation indicated by each algebraic rule.

Name: ______Period: ______Date: ______

  1. (x, y) → (x – 2, y + 1)
  1. (x, y) → (x, – y)
  1. (x, y) → (– x, y)
  1. (x, y) → (– y, x)
  1. (x, y) → (y, – x)
  1. (x, y) → (2x, 2y)
  1. (x, y) → (– x, – y)
  1. (x, y) → (x, y)

  1. The table shows the coordinates of parallelogram RSTU and parallelogram R′S′T′U′ after a transformation. What type of transformation does the table represent? Write the algebraic rule for the transformation. What are the coordinates of vertex R′?
  1. Quadrilateral ABCD is reflected over the x-axis. Write the algebraic rule for the transformation and determine the new coordinates for Quadrilateral A’B’C’D’. Graph the new image.
  1. Polygon PQRSTU is shown on the coordinate grid below. The polygon is rotated 90 degrees clockwise about the origin. Write an algebraic representation that explains the effect of the transformation. What are the new coordinates of the polygon?
  1. Sophia is drawing triangles for an art project. Which algebraic representation describes the transformation of ∆ABC to ∆A′B′C′ ?

A(x, y) → (–x – 3, y + 5)

B(x, y) → (x + 3, y + 5)

C(x, y) → (–x + 3, y + 3)

D(x, y) → (x + 3, –y + 3)

  1. Rectangle QRST with vertices Q(–2, –4), R(–2, 1),

S(–4, 1), and T(–4, –4) is rotated about the origin 180°, reflected over the x-axis, and then translated 1 unit right and 2 units up. Determine the new coordinates of the rectangle’s vertices.

  1. Dolly went to the rodeo carnival. From the main entrance she used the algebraic representation

(x, y) → (x – 3, y + 8) to walk to a ride. Which ride did Dolly walk to?

  1. The table shows the coordinates of triangle ABC and triangle A′B′C′ after a transformation. Which statement is true?
  1. Triangle ABC is translated to create rectangle A′B′C′. The triangles are congruent.
  2. Triangle ABC is rotated about the origin to create triangle A′B′C′. The triangles are congruent.
  3. Triangle ABC is translated to create triangle A′B′C′. The triangles are not congruent.
  4. Triangle ABC is rotated about the origin to create triangle A′B′C′. The triangles are not congruent.

  1. Which transformation does not preserve congruence?
  1. Translation
  2. Reflection
  3. Rotation
  4. Dilation
  1. Are all similar figures congruent? Explain.

Use the similar polygons below to answer #18-19.

  1. Write congruence statements comparing the corresponding parts of the triangles.
  1. Determine the missing side measure x.
  1. A 10-foot-tall tree casts a shadow that is 16 feet long. A 4-foot-tall child is standing next to the tree. About how long is the shadow of the child?