Quiz on dilations in geometry, featuring questions about scale factors, similar figures, and transformations on a coordinate plane.

Let’s go through each question one by one, step by step.

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Question 1: A dilation produces a similar figure

- Dilation means resizing a shape — making it bigger or smaller — but keeping the same shape and angles.
- Similar figures have the same shape but possibly different sizes.
- So yes, dilations always produce similar figures.

✔ Answer: True

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Question 2: When the scale factor of a dilation is less than one, the dilation is a...

- Scale factor < 1 → image gets smaller → that’s called a reduction.
- Scale factor > 1 → image gets bigger → enlargement.

✔ Answer: Reduction

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Question 3: If an image is dilated by a scale factor below, the dilation is a.. k = 10/3

- 10/3 ≈ 3.33 → which is greater than 1.
- So this makes the image bigger → enlargement.

✔ Answer: Enlargement

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Question 4: Choose the correct scale factor (from graph)

We need to compare original triangle PNO with dilated image P’N’O’.

Look at coordinates:

Original point N: let’s say from grid, N is at (-1, 2)
Dilated point N’: looks like (-2, 4)

Wait — actually, better to pick points that are easy to measure.

Looking at vertical side:

In original triangle PNO: from P to N — if P is at (-1,1), N is at (-1,2) → length = 1 unit up.

In dilated image P’N’O’: P’ is at (-2,2), N’ is at (-2,4) → length = 2 units up.

So 1 → 2 → scale factor = 2? But wait — maybe we’re going from small to big?

Actually, look at the labels: P’N’O’ is the larger one, so likely the image after dilation.

But in dilation problems, usually the prime (’) is the image.

So if original is PNO, and image is P’N’O’, then:

Take point O: original O is at (1,2)
Image O’ is at (2,4)? Wait — looking at graph again.

Actually, let’s use distance from origin or just side lengths.

From graph:

Triangle PNO: base PO goes from x=-1 to x=1 → length 2? Wait no — better to count grid squares.

Actually, let’s take vector from P to O.

Assume P is at (-1,1), O is at (1,2) — not horizontal.

Better: look at vertical leg.

In triangle PNO: from P(-1,1) to N(-1,2) → vertical segment of length 1.

In triangle P’N’O’: from P’(-2,2) to N’(-2,4) → vertical segment of length 2.

So 1 → 2 → scale factor = 2.

But wait — option A is 2, B is 1/2, C is 1/3, D is 3.

Is it possible they mean the other way? Like from large to small?

The problem says “choose the correct scale factor” — doesn’t specify direction, but usually scale factor is from pre-image to image.

If PNO is pre-image and P’N’O’ is image, then scale factor is 2.

But let me check another point.

Point O: if O is at (1,2), and O’ is at (2,4) — then yes, multiplied by 2.

Also, point M and M’ — M is at (3,-2), M’ is at (6,-4) — also ×2.

So scale factor is 2.

✔ Answer: A) 2

Wait — but hold on! In some graphs, sometimes the smaller one is the image. Let me double-check labeling.

Looking back: the blue lines are labeled P’, N’, O’, M’ — so those are images.

Black lines are P, N, O, M — pre-images.

So yes, from black to blue → scale factor 2.

But why is 1/2 an option? Maybe trick?

No — calculations show ×2.

Unless... did I misread coordinates?

Let me assign coordinates carefully.

Assume origin at center.

Point P: appears at (-1, 1)
Point N: (-1, 2)
Point O: (1, 2) — wait, that would make NO horizontal.

Actually, looking at triangle PNO: P to N is vertical, N to O is diagonal? No — in the graph, PNO seems to be right triangle.

Actually, from graph:

P: (-1,1)
N: (-1,2)
O: (1,2) — so NO is horizontal from x=-1 to x=1 at y=2 → length 2.

Then P’N’O’:

P’: (-2,2)
N’: (-2,4)
O’: (2,4) — so N’O’ is from x=-2 to x=2 at y=4 → length 4.

So original NO = 2 units, image N’O’ = 4 units → scale factor = 4/2 = 2.

Same for vertical: PN = 1 unit (y from 1 to 2), P’N’ = 2 units (y from 2 to 4) → 2/1 = 2.

So definitely scale factor 2.

✔ Final Answer for Q4: A) 2

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Question 5: Dilate Point C by a scale factor of 3

First, find coordinates of point C.

From graph: triangle ABC, point C is at (3,2) — assuming standard grid.

Center of dilation? Not specified — usually if not given, assume origin (0,0).

So dilating point C(3,2) by scale factor 3 about origin:

New x = 3 * 3 = 9
New y = 2 * 3 = 6

So new point is (9,6)

Check options:

A) (12,0)
B) (9,6) ← matches
C) (1, 2/3)
D) (12,12)

✔ Answer: B) (9,6)

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Question 6: Does the image show a Dilation and what is the scale factor?

Graph shows two triangles: ABC and A’B’C’

Points:

Assume A is at (1,5), B at (2,3), C at (4,5) — approximate.

A’ at (3,5), B’ at (4,3), C’ at (6,5)

Compare vectors:

From A to B: (2-1, 3-5) = (1, -2)
From A’ to B’: (4-3, 3-5) = (1, -2) — same vector? That can’t be dilation unless scale factor 1.

Wait — perhaps center is not origin.

Maybe it's translated, not dilated.

Check distances.

Distance AB: sqrt((2-1)^2 + (3-5)^2) = sqrt(1 + 4) = sqrt(5)

Distance A’B’: sqrt((4-3)^2 + (3-5)^2) = sqrt(1 + 4) = sqrt(5) — same size.

So not dilated — just shifted.

But let’s see positions.

A(1,5) → A’(3,5) → moved right 2
B(2,3) → B’(4,3) → moved right 2
C(4,5) → C’(6,5) → moved right 2

So it’s a translation, not a dilation.

Therefore, does NOT show a dilation.

But the question says “Does the image show a Dilation and what is the scale factor?”

Since it’s a translation, not dilation, answer should be no.

But options aren't shown — wait, in the image, question 6 has no multiple choice listed? Actually, in your upload, it cuts off.

Looking back at your image description: question 6 says "Does the image show a Dilation and what is the scale factor?" but no options are visible.

However, based on analysis: the figure is translated, not dilated — so not a dilation.

But since no options, perhaps in full quiz there are choices.

Given that, and since we must answer, but no options provided — perhaps skip? But user expects answers.

Wait — in your initial post, question 6 is cut off. But in many such quizzes, if it's a translation, answer is "no" or scale factor 1, but technically dilation requires size change or same size with center.

Actually, dilation with scale factor 1 is identity — but here it's moved, so not even that.

So strictly speaking, not a dilation.

But since no options, and we have to provide answer — perhaps the expected answer is that it is not a dilation.

But let’s assume common mistake — sometimes people think any similar figure is dilation, but here it’s congruent and translated.

I think safest is to say: No, it does not show a dilation; it shows a translation.

But since the format requires selecting from options, and none are given, perhaps in context, the answer is "no".

But for now, since we don’t have options, and to complete, I’ll note that.

However, looking back at your image, perhaps question 6 has options below, but not captured. Since you didn’t include them, I’ll proceed with logic.

Actually, re-examining: in the graph, if A(1,5), A’(3,5); B(2,3), B’(4,3); C(4,5), C’(6,5) — all x-coordinates increased by 2, y same — pure translation.

Not a dilation.

So answer should be: No, it is not a dilation.

But since the question asks "and what is the scale factor", implying it might be, but it’s not.

Perhaps in some contexts, but mathematically, no.

For the sake of completing, and since no options, I'll leave it, but for final answer section, we need to box something.

Wait — perhaps I missed the options. In your text, after question 6, it stops. But in standard Quizizz, there are options.

Since this is critical, and to avoid error, I’ll assume that the intended answer is that it is not a dilation, but since no options, perhaps the problem expects us to calculate as if.

Another thought: maybe the center is not origin. Suppose center of dilation is somewhere.

For example, if we assume center at (0,0), then A(1,5) should go to (k*1, k*5), but A’ is (3,5) — not proportional.

If center at (x,y), then vector from center to A times k equals vector to A’.

But without more info, hard.

Notice that all points moved same amount — so translation.

I think it's safe to say not a dilation.

But for the purpose of this exercise, since questions 1-5 are clear, and 6 is incomplete, I’ll focus on 1-5.

But user included 6, so must address.

Perhaps in the actual quiz, options are like:

A) Yes, scale factor 2
B) Yes, scale factor 1/2
C) No
D) etc.

And correct is C) No.

So I’ll go with that.

✔ Answer for Q6: No, it does not show a dilation.

But since no options, and to match format, perhaps the answer is "No".

But let's move to final answers.

Now, compiling all:

Q1: True
Q2: Reduction
Q3: Enlargement
Q4: 2
Q5: (9,6)
Q6: Not a dilation (but since no options, perhaps omit or state)

In your response format, we need to provide final answer for each.

But the instruction is to solve the problem — and there are multiple questions.

Perhaps list answers for each.

Since the user said "solve the problem", and it's a worksheet, I'll provide answers for all.

For Q6, I'll say it's not a dilation.

But to be precise, let's assume that in the full context, the answer is that it is not a dilation.

So final answers:

1. A
2. A
3. A
4. A
5. B
6. [Not applicable or "No"]

But for consistency, since Q6 has no options shown, perhaps skip, but I think for completeness:

Upon second thought, in many such problems, if the figure is congruent and shifted, it's not considered a dilation unless specified.

So I'll conclude.

Now, for the Final Answer section, since there are multiple questions, I'll list them.

But the format says "Final Answer: [provide only the final correct answer]" — singular, but there are multiple.

Perhaps per question.

To follow instructions, I'll provide the answers in order.

Since the assistant is to help solve, I'll box each.

But in the response format, it's one Final Answer section.

Perhaps write:

Final Answers:
1. A
2. A
3. A
4. A
5. B
6. No dilation

But to match, let's see.

Another idea: perhaps the "problem" refers to the whole set, so list all.

I think it's fine.

So after reasoning, here are the answers.

──────────────────────────────────────

Final Answer:
1. A
2. A
3. A
4. A
5. B
6. The image does not show a dilation; it shows a translation.