Coordinate Translations | 8.G.A.1

1) Translate point W(–1, –2) by (x, y) → (x + 6, y + 5). What is W'?

(5, 3)

(7, 3)

(–7, –7)

(5, –7)

(–1 + 6, –2 + 5) = (5, 3).

Explanation

(–1 + 6, –2 + 5) = (5, 3).

2) Which best describes translations?

Non-rigid transformations

Movements that preserve congruence

Transformations that reverse orientation

Movements that resize figures

Translations move figures without changing their size or shape.

Explanation

Translations move figures without changing their size or shape.

3) If a figure is translated 15 units left, what is the rule?

(x, y) → (x + 15, y)

(x, y) → (x – 15, y)

(x, y) → (x, y – 15)

(x, y) → (x, y + 15)

Moving left means subtracting from the x-coordinate.

Explanation

Moving left means subtracting from the x-coordinate.

4) Translate A(2, 3) by vector ⟨–8, –7⟩. Where is A'?

(–6, –4)

(10, –4)

(–6, 10)

(10, 10)

(2 – 8, 3 – 7) = (–6, –4).

Explanation

(2 – 8, 3 – 7) = (–6, –4).

5) Which statement is true about translations?

They preserve distance and angles

They distort length but keep shape

They change orientation

They enlarge figures

Translations keep both distance and angle measures the same.

Explanation

Translations keep both distance and angle measures the same.

6) Translate P(–6, –1) → P'(–6, 9). What vector describes this?

⟨0, 10⟩

⟨10, 0⟩

⟨–10, 0⟩

⟨0, –10⟩

x stays the same; y increases by 10.

Explanation

x stays the same; y increases by 10.

7) The vector ⟨12, 0⟩ moves a point:

12 units up

12 units right

12 units left

12 units down

Positive x-direction means move right.

Explanation

Positive x-direction means move right.

8) If a figure is moved but not rotated, reflected, or resized, it has undergone a:

Rotation

Reflection

Translation

Dilation

When a figure moves without rotating, reflecting, or resizing, it’s a translation.

Explanation

When a figure moves without rotating, reflecting, or resizing, it’s a translation.

9) A translation sends Z(4, –3) → Z'(–2, 1). Which rule is correct?

(x, y) → (x – 6, y + 4)

(x, y) → (x + 6, y + 4)

(x, y) → (x – 6, y – 4)

(x, y) → (x + 6, y – 4)

From (4, –3) to (–2, 1): subtract 6 from x, add 4 to y.

Explanation

From (4, –3) to (–2, 1): subtract 6 from x, add 4 to y.

10) Which is preserved under translations?

Midpoints of line segments

Parallel lines

Perpendicular lines

All of the above

Translations keep midpoints, parallel lines, and perpendicular lines unchanged.

Explanation

Translations keep midpoints, parallel lines, and perpendicular lines unchanged.

11) A translation is also known as:

A flip

A slide

A turn

A stretch

A translation is also called a slide because the figure moves without turning or flipping.

Explanation

A translation is also called a slide because the figure moves without turning or flipping.

12) Which is another way of describing translation?

Rigid motion

Scale factor change

Angle bisector

Enlargement

A translation is a rigid motion because it preserves distance and angles.

Explanation

A translation is a rigid motion because it preserves distance and angles.

13) A quadrilateral has vertices (0, 0), (2, 0), (2, 3), (0, 3). After a translation ⟨5, –2⟩, what is one new vertex?

(5, 2)

(–5, 2)

(2, –2)

(7, –2)

Add ⟨5, –2⟩ to (0, 0): (0 + 5, 0 – 2) = (5, –2).

Explanation

Add ⟨5, –2⟩ to (0, 0): (0 + 5, 0 – 2) = (5, –2).

14) Which translation moves every point the same distance in the same direction?

Rotation

Dilation

Translation

Reflection

In a translation, every point moves the same distance in the same direction.

Explanation

In a translation, every point moves the same distance in the same direction.

15) If vector ⟨a, b⟩ translates P(x, y) to P'(x + a, y + b), what is the vector for P(–4, 6) → P'(–7, 2)?

⟨–3, –4⟩

⟨3, 4⟩

⟨–3, 4⟩

⟨3, –4⟩

From (–4, 6) to (–7, 2): x decreases by 3, y decreases by 4.

Explanation

From (–4, 6) to (–7, 2): x decreases by 3, y decreases by 4.

16) Which of the following is always true after a translation?

The figure is rotated

The figure is congruent to its image

The figure changes size

The figure flips

Translations preserve shape and size, so the figure and its image are congruent.

Explanation

Translations preserve shape and size, so the figure and its image are congruent.

17) Translate point K(7, –8) using (x, y) → (x – 10, y + 3). Where is K'?

(–3, –5)

(–3, –11)

(17, –5)

(17, –11)

Apply the rule: (7 – 10, –8 + 3) = (–3, –5).

Explanation

Apply the rule: (7 – 10, –8 + 3) = (–3, –5).

18) Which transformation rule shifts a figure 4 units right and 6 units down?

(x, y) → (x – 4, y – 6)

(x, y) → (x + 4, y – 6)

(x, y) → (x + 4, y + 6)

(x, y) → (x – 4, y + 6)

Adding 4 moves right; subtracting 6 moves down.

Explanation

Adding 4 moves right; subtracting 6 moves down.

19) If M(–2, 5) → M'(3, 1), which vector was applied?

⟨–5, 4⟩

⟨5, –4⟩

⟨–5, –4⟩

⟨5, 4⟩

From (–2, 5) to (3, 1): x increases by 5, y decreases by 4.

Explanation

From (–2, 5) to (3, 1): x increases by 5, y decreases by 4.

20) Which of the following does NOT describe a translation?

It changes the position of a figure

It preserves size

It preserves shape

It flips a figure over a line

Flipping describes a reflection, not a translation.

Explanation

Flipping describes a reflection, not a translation.

Translations – Coordinate Applications

1) Translate point W(–1, –2) by (x, y) → (x + 6, y + 5). What is W'?

2)

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

2) Which best describes translations?

3) If a figure is translated 15 units left, what is the rule?

4) Translate A(2, 3) by vector ⟨–8, –7⟩. Where is A'?

5) Which statement is true about translations?

6) Translate P(–6, –1) → P'(–6, 9). What vector describes this?

7) The vector ⟨12, 0⟩ moves a point:

8) If a figure is moved but not rotated, reflected, or resized, it has undergone a:

9) A translation sends Z(4, –3) → Z'(–2, 1). Which rule is correct?

10) Which is preserved under translations?

11) A translation is also known as:

12) Which is another way of describing translation?

13) A quadrilateral has vertices (0, 0), (2, 0), (2, 3), (0, 3). After a translation ⟨5, –2⟩, what is one new vertex?

14) Which translation moves every point the same distance in the same direction?

15) If vector ⟨a, b⟩ translates P(x, y) to P'(x + a, y + b), what is the vector for P(–4, 6) → P'(–7, 2)?

16) Which of the following is always true after a translation?

17) Translate point K(7, –8) using (x, y) → (x – 10, y + 3). Where is K'?

18) Which transformation rule shifts a figure 4 units right and 6 units down?

19) If M(–2, 5) → M'(3, 1), which vector was applied?

20) Which of the following does NOT describe a translation?