Translation

Given: Triangle ABC with vertices A(-3,5), B(-2,2), and C(-4,2)

Given: Triangle A'B'C' with vertices A'(3,1), B'(4,-2), and C'(2,-2).

Write the rule to map Triangle ABC onto Triangle A'B'C'

A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down. Which rule describes the translation?

• (x, y) → (x + 3, y – 4)

• (x, y) → (x + 3, y + 4)

• (x, y) → (x + 4, y – 3)

• (x, y) → (x + 4, y + 3)

Assume each figure shown has the same orientation. Which figure is the image of square LMNP after a translation of

(x, y) → (x + 5, y – 3)?

• 1

• 2

• 3

• 4

Triangle QRS has vertices Q (8, –6), R(10, 5), and S(–3, 3). What are the coordinates of the vertices of the image of the triangle after a translation of

T_{–7.6, 4.3}(x, y)?

• Q’= (0.4 ,- 1.7)

  R’= (2.4,9.3)

  S’= (-10.6,7.3)

• Q’= (1.4 ,1.7)

  R’= (3,9)

  S’= (-10,7.3)

• Q’= (0.4 ,- 1.7)

  R’= (2.1,7.2)

  S’= (-10.6,7.3)

• Q’= (0.4 ,- 1.7)

  R’= (2.4,9.3)

  S’= (1.4,1.7)

A graphic designer wants to translate rectangle DEFG using T_{–1, 2}(x, y). The pre-image has coordinates D(–1, 3), E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?

• a)

• b)

• c)

• d)

Li transformed rectangle ABCD. The image is shown. Does Li’s transformation represent a translation?

• Yes, the image represents a translation.

• No, the image does not have the same size.

• No, the image does not have the same orientation.

• a) No, the image does not have the same shape.

The image of trapezoid ABCD has coordinates

A′(–2, –5), B′(–1, –2), C′(2, –2), and D′(3, –5). It was translated by the rule T_{–1, –3}(x, y). Which diagram shows the pre-image?

• A

• B

• C

• D

Triange ABC is translated to image A’B’C’. In this translation, A(5,1) maps to A’(6,-2). The coordinates of B’ are (-1,0). What are the coordinates of B?

• B( 2 , -3)

• B( -2 , -3)

• B( 2, 3)

• B(-2 , 3 )

Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options.

• The rule for the translation can be written as T_{–5, 3}(x, y).

• The rule for the translation can be written as T_{3, –5}(x, y).

• The rule for the translation can be written as (x, y)→(x + 3,y – 3).

• The rule for the translation can be written as

  (x, y) → (x – 3, y – 3).

• Triangle ABC has been translated 3 units to the right and 5 units down.

Trapezoid L'M'N'P' was constructed using trapezoid LMNP.

For the transformation to be a translation, which statements must be true? Select four options.

• LL'=PP'

• LL'=MM'

• Trapezoid LMNP is congruent to trapezoid L'M'N'P'.

• NN'=1/2 PP'

• All line segments that connect a point on the pre-image to its corresponding point on the image are parallel.