Congruence Through Translations

1) Which statement is always true?

Translations change figure size

Translations create congruent figures

Translations flip figures over lines

Translations distort shapes

They preserve size and shape.

Explanation

They preserve size and shape.

2) If T(–3, 9) → T'(–3, 0), what is the translation vector?

⟨0, 9⟩

⟨0, –9⟩

⟨–9, 0⟩

⟨9, 0⟩

From (–3, 9) to (–3, 0): x change = 0, y change = –9.

Explanation

From (–3, 9) to (–3, 0): x change = 0, y change = –9.

3) A figure is congruent to its image after translation because:

Corresponding sides are proportional

Corresponding angles change

Distances and angles are preserved

Only slopes are preserved

That is the defining property of translations.

Explanation

That is the defining property of translations.

4) Translate A(5, 5) by ⟨–12, 0⟩. Where is A'?

(–7, 5)

(7, 5)

(17, 5)

(–17, 5)

A(5, 5) + ⟨–12, 0⟩ = (–7, 5).

Explanation

A(5, 5) + ⟨–12, 0⟩ = (–7, 5).

5) Which of the following describes two congruent figures?

One is the reflection of the other

One is the translation of the other

One is the rotation of the other

All of the above

Reflections, translations, and rotations all map congruent figures.

Explanation

Reflections, translations, and rotations all map congruent figures.

6) Pentagon JKLMP is translated by (x, y) → (x – 2, y + 4). Which is true about the image?

It is not congruent

It is congruent and moved left and up

It is larger

It is rotated

Rule (x – 2, y + 4) shifts left 2 and up 4 with no size change.

Explanation

Rule (x – 2, y + 4) shifts left 2 and up 4 with no size change.

7) Which vector moves a point 9 units down?

⟨9, 0⟩

⟨0, –9⟩

⟨–9, 0⟩

⟨0, 9⟩

Down 9 changes only y by –9.

Explanation

Down 9 changes only y by –9.

8) Which of the following transformations would not preserve congruence?

Translation

Rotation

Reflection

Dilation

Dilations change size, so they do not preserve congruence.

Explanation

Dilations change size, so they do not preserve congruence.

9) Why do translations prove congruence?

They change distances equally

They preserve lengths and angles exactly

They distort orientation

They shrink figures proportionally

That is why a translation proves congruence.

Explanation

That is why a translation proves congruence.

10) The translation ⟨8, –3⟩ is applied to E(–2, 7). Where is E'?

(10, 4)

(6, 4)

(–10, 10)

(–10, 4)

E(–2, 7) + ⟨8, –3⟩ = (–2 + 8, 7 – 3) = (6, 4).

Explanation

E(–2, 7) + ⟨8, –3⟩ = (–2 + 8, 7 – 3) = (6, 4).

11) Which transformation best demonstrates that two polygons are congruent?

Translation

Stretching

Scaling

Shearing

A translation slides a figure without turning or resizing, so it shows congruence.

Explanation

A translation slides a figure without turning or resizing, so it shows congruence.

12) Rectangle WXYZ has vertices at W(0,0), X(4,0), Y(4,3), Z(0,3). It is translated by (x, y) → (x + 2, y – 5). Where is Z'?

(2, –2)

(–2, –5)

(2, 8)

(–2, 8)

Z(0, 3) → (0 + 2, 3 – 5) = (2, –2).

Explanation

Z(0, 3) → (0 + 2, 3 – 5) = (2, –2).

13) What vector maps D(7, –2) to D'(3, 4)?

⟨–4, 6⟩

⟨4, –6⟩

⟨–10, 6⟩

⟨6, –4⟩

From (7, –2) to (3, 4): x change = 3 – 7 = –4, y change = 4 – (–2) = 6.

Explanation

From (7, –2) to (3, 4): x change = 3 – 7 = –4, y change = 4 – (–2) = 6.

14) Which figure cannot be mapped onto its congruent copy by translation alone?

A rotated square

A translated triangle

A shifted circle

A moved parallelogram

A rotated copy needs a rotation, not just a translation.

Explanation

A rotated copy needs a rotation, not just a translation.

15) If translations preserve congruence, what is always true?

Corresponding sides are equal

Corresponding angles are equal

Figures overlap exactly after translation

All of the above

Translations keep corresponding sides and angles equal, and images overlap after sliding.

Explanation

Translations keep corresponding sides and angles equal, and images overlap after sliding.

16) A translation moves a figure 6 units up and 4 units left. Which rule describes this?

(x, y) → (x + 4, y – 6)

(x, y) → (x – 4, y + 6)

(x, y) → (x + 6, y – 4)

(x, y) → (x – 6, y + 4)

Left means subtract 4 from x. Up means add 6 to y.

Explanation

Left means subtract 4 from x. Up means add 6 to y.

17) Triangle PQR has vertices at P(–1,2), Q(2,2), R(0,5). It is translated using ⟨–3, –2⟩. Where is Q'?

(–1, 0)

(–1, –4)

(5, 0)

(–5, 0)

Apply ⟨–3, –2⟩ to Q(2, 2): (2 – 3, 2 – 2) = (–1, 0).

Explanation

Apply ⟨–3, –2⟩ to Q(2, 2): (2 – 3, 2 – 2) = (–1, 0).

18) Which of the following does a translation NOT preserve?

Angle measures

Orientation

Position

Congruence

Translations preserve angles, orientation, and congruence. Only position changes.

Explanation

Translations preserve angles, orientation, and congruence. Only position changes.

19) Translations are considered what type of transformation?

Rigid

Non-rigid

Distorting

Enlarging

Translations are rigid motions. They keep lengths and angles the same.

Explanation

Translations are rigid motions. They keep lengths and angles the same.

20) If A(0, 4) → A'(0, –3), which translation vector is correct?

⟨0, –7⟩

⟨0, 7⟩

⟨–7, 0⟩

⟨7, 0⟩

From (0, 4) to (0, –3): x change = 0, y change = –3 – 4 = –7.

Explanation

From (0, 4) to (0, –3): x change = 0, y change = –3 – 4 = –7.

Congruence Through Translations

1) Which statement is always true?

2)

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

2) If T(–3, 9) → T'(–3, 0), what is the translation vector?

3) A figure is congruent to its image after translation because:

4) Translate A(5, 5) by ⟨–12, 0⟩. Where is A'?

5) Which of the following describes two congruent figures?

6) Pentagon JKLMP is translated by (x, y) → (x – 2, y + 4). Which is true about the image?

7) Which vector moves a point 9 units down?

8) Which of the following transformations would not preserve congruence?

9) Why do translations prove congruence?

10) The translation ⟨8, –3⟩ is applied to E(–2, 7). Where is E'?

11) Which transformation best demonstrates that two polygons are congruent?

12) Rectangle WXYZ has vertices at W(0,0), X(4,0), Y(4,3), Z(0,3). It is translated by (x, y) → (x + 2, y – 5). Where is Z'?

13) What vector maps D(7, –2) to D'(3, 4)?

14) Which figure cannot be mapped onto its congruent copy by translation alone?

15) If translations preserve congruence, what is always true?

16) A translation moves a figure 6 units up and 4 units left. Which rule describes this?

17) Triangle PQR has vertices at P(–1,2), Q(2,2), R(0,5). It is translated using ⟨–3, –2⟩. Where is Q'?

18) Which of the following does a translation NOT preserve?

19) Translations are considered what type of transformation?

20) If A(0, 4) → A'(0, –3), which translation vector is correct?