Translations: Rules & Properties | 8.G.A.1

1) Translate B(–3, –1) by (x, y) → (x + 2, y + 5). Where is B'?

(–1, 4)

(–5, 4)

(–1, –6)

(–5, –6)

Rule (x + 2, y + 5): (–3 + 2, –1 + 5) = (–1, 4).

Explanation

Rule (x + 2, y + 5): (–3 + 2, –1 + 5) = (–1, 4).

2) Which property is preserved after a translation?

Distance between points

Angle measures

Shape and size

All of the above

Translations keep distance, angles, shape, and size the same—so all these properties are preserved.

Explanation

Translations keep distance, angles, shape, and size the same—so all these properties are preserved.

3) Which vector represents a movement of 5 units right and 2 units down?

⟨–5, 2⟩

⟨5, –2⟩

⟨2, 5⟩

⟨–2, –5⟩

Positive 5 = 5 right; negative 2 = 2 down.

Explanation

Positive 5 = 5 right; negative 2 = 2 down.

4) The vector ⟨–6, 0⟩ moves a point:

6 units right

6 units left

6 units up

6 units down

Negative x direction = move left.

Explanation

Negative x direction = move left.

5) The translation rule (x, y) → (x – 3, y + 7) moves a point:

3 units right and 7 units up

3 units right and 7 units down

3 units left and 7 units up

3 units left and 7 units down

Subtracting 3 moves left, adding 7 moves up.

Explanation

Subtracting 3 moves left, adding 7 moves up.

6) Which of the following best describes a translation?

A figure is flipped over a line

A figure slides without turning

A figure is rotated around a point

A figure is enlarged

A translation means the figure moves (slides) to a new position without rotating or flipping.

Explanation

A translation means the figure moves (slides) to a new position without rotating or flipping.

7) Which figure will remain congruent to its preimage after translation?

Only squares

Only circles

All polygons

Only right triangles

Every figure keeps its size and shape after a translation.

Explanation

Every figure keeps its size and shape after a translation.

8) A triangle with vertices (0, 0), (2, 1), and (1, 3) is translated by ⟨–4, –2⟩. Which is one vertex after translation?

(–4, –2)

(–2, –1)

(3, –2)

(–2, 1)

(0 – 4, 0 – 2) = (–4, –2). That’s one translated vertex.

Explanation

(0 – 4, 0 – 2) = (–4, –2). That’s one translated vertex.

9) A figure is moved 8 units left and 2 units down. Which rule describes this?

(x, y) → (x – 8, y – 2)

(x, y) → (x + 8, y – 2)

(x, y) → (x – 8, y + 2)

(x, y) → (x + 8, y + 2)

Left means subtract 8 from x; down means subtract 2 from y.

Explanation

Left means subtract 8 from x; down means subtract 2 from y.

10) If point A(2, –5) is translated by (x, y) → (x + 6, y + 4), what are the coordinates of A'?

(8, –9)

(8, –1)

(–4, –1)

(–4, –9)

Rule (x + 6, y + 4): (2 + 6, –5 + 4) = (8, –1).

Explanation

Rule (x + 6, y + 4): (2 + 6, –5 + 4) = (8, –1).

11) Which transformation undoes a translation by vector ⟨a, b⟩?

A translation by vector ⟨a, b⟩

A translation by vector ⟨–a, –b⟩

A reflection across the x-axis

A rotation of 180° about the origin

To undo a translation, move in the exact opposite direction.

Explanation

To undo a translation, move in the exact opposite direction.

12) Which statement is true?

Translations preserve congruence

Translations distort figures

Translations only apply to polygons

Translations reverse orientation

They keep shape and size the same, so figures remain congruent.

Explanation

They keep shape and size the same, so figures remain congruent.

13) A rectangle slides without turning. This is an example of:

Translation

Reflection

Rotation

Dilation

Sliding without turning is the definition of translation.

Explanation

Sliding without turning is the definition of translation.

14) Which transformation is equivalent to two consecutive translations?

A single translation

Reflection

Rotation

Dilation

Two translations combine into one equivalent translation.

Explanation

Two translations combine into one equivalent translation.

15) The image of point P(–1, 4) is P'(–6, 9). What translation rule was applied?

(x, y) → (x – 5, y + 5)

(x, y) → (x + 5, y + 5)

(x, y) → (x – 7, y – 5)

(x, y) → (x + 7, y – 5)

From (–1, 4) to (–6, 9): subtract 5 from x and add 5 to y.

Explanation

From (–1, 4) to (–6, 9): subtract 5 from x and add 5 to y.

16) Which of the following is not true about translations?

They preserve parallelism

They preserve orientation

They change side lengths

They slide figures without rotation

Translations do not change side lengths—this statement is false.

Explanation

Translations do not change side lengths—this statement is false.

17) Which vector would map C(2, 7) to C'(–1, 3)?

⟨–3, –4⟩

⟨3, –4⟩

⟨–3, 4⟩

⟨3, 4⟩

From (2, 7) to (–1, 3): x decreases by 3, y decreases by 4.

Explanation

From (2, 7) to (–1, 3): x decreases by 3, y decreases by 4.

18) Which of these would NOT be preserved by a translation?

Orientation

Distance

Area

Position

Translations change the location (position) but not orientation, distance, or area.

Explanation

Translations change the location (position) but not orientation, distance, or area.

19) If Q(5, –3) → Q'(10, –3), what is the vector?

⟨5, 0⟩

⟨–5, 0⟩

⟨0, –5⟩

⟨0, 5⟩

From (5, –3) to (10, –3): +5 in x direction, no change in y.

Explanation

From (5, –3) to (10, –3): +5 in x direction, no change in y.

20) If a translation is represented by vector ⟨0, 0⟩, the transformation is:

Reflection

Rotation

Identity

Dilation

Vector ⟨0, 0⟩ means no movement—the figure stays in place.

Explanation

Vector ⟨0, 0⟩ means no movement—the figure stays in place.

Translations – Rules and Properties

1) Translate B(–3, –1) by (x, y) → (x + 2, y + 5). Where is B'?

2)

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

2) Which property is preserved after a translation?

3) Which vector represents a movement of 5 units right and 2 units down?

4) The vector ⟨–6, 0⟩ moves a point:

5) The translation rule (x, y) → (x – 3, y + 7) moves a point:

6) Which of the following best describes a translation?

7) Which figure will remain congruent to its preimage after translation?

8) A triangle with vertices (0, 0), (2, 1), and (1, 3) is translated by ⟨–4, –2⟩. Which is one vertex after translation?

9) A figure is moved 8 units left and 2 units down. Which rule describes this?

10) If point A(2, –5) is translated by (x, y) → (x + 6, y + 4), what are the coordinates of A'?

11) Which transformation undoes a translation by vector ⟨a, b⟩?

12) Which statement is true?

13) A rectangle slides without turning. This is an example of:

14) Which transformation is equivalent to two consecutive translations?

15) The image of point P(–1, 4) is P'(–6, 9). What translation rule was applied?

16) Which of the following is not true about translations?

17) Which vector would map C(2, 7) to C'(–1, 3)?

18) Which of these would NOT be preserved by a translation?

19) If Q(5, –3) → Q'(10, –3), what is the vector?

20) If a translation is represented by vector ⟨0, 0⟩, the transformation is: