Dilations Worksheets - TheWorksheets.CoM - TheWorksheets Library - Free Printable

Let’s go through each problem step by step. We’re looking at dilations — that means shapes getting bigger or smaller from a center point (usually the origin, unless told otherwise). The scale factor tells us how much it changes:

- If scale factor > 1 → enlargement
- If scale factor = 1 → same size (not really a dilation in most cases)
- If 0 < scale factor < 1 → reduction
- If scale factor is negative → also flips the shape over the center point, but we still call it enlargement or reduction based on absolute value.

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Problem 1: Identify type of dilation for given scale factors

a) Scale factor = 3
→ 3 > 1 → enlargement

b) Scale factor = 1/2
→ 0 < 1/2 < 1 → reduction

c) Scale factor = 5/4 = 1.25
→ 1.25 > 1 → enlargement

d) Scale factor = 0.75
→ 0 < 0.75 < 1 → reduction

e) Scale factor = 2.5
→ 2.5 > 1 → enlargement

f) Scale factor = 1/3 ≈ 0.333
→ 0 < 1/3 < 1 → reduction

✔ So answers are:
a) enlargement
b) reduction
c) enlargement
d) reduction
e) enlargement
f) reduction

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Problem 2: Look at graphs and decide if transformation is enlargement or reduction

We compare original figure to image (the transformed one). Count units or look at side lengths.

#### Graph a: Triangle ABC → A’B’C’

Original triangle has base about 2 units, height about 2 units.
Image triangle has base about 4 units, height about 4 units.
→ Doubled in size → enlargement

#### Graph b: Rectangle → Image rectangle

Original: width 2, height 3
Image: width 4, height 6
→ Both doubled → enlargement

Wait — actually, let me double-check graph b.

Looking again: Original rectangle goes from x=1 to x=3 (width 2), y=1 to y=4 (height 3).
Image goes from x=2 to x=6 (width 4), y=2 to y=8 (height 6).
Yes, both dimensions doubled → scale factor 2 → enlargement

But wait — the answer key says “reducer” for b? That can’t be right unless I misread.

Hold on — maybe I mixed up which is original and which is image?

In graph b: The small rectangle is labeled with points like (1,1), (3,1), etc. The big one is labeled with primes? Actually, no — in the image, the small one is drawn first, then the large one is the image? Or vice versa?

Actually, looking at standard convention: usually the unprimed is original, primed is image.

In graph b: The small rectangle has coordinates like (1,1), (3,1), (3,4), (1,4) — that’s original.

The image has points like (2,2), (6,2), (6,8), (2,8) — so yes, scaled by 2 → enlargement.

But the handwritten answer says “reducer” — that must be a mistake? Or did they mean something else?

Wait — perhaps in some contexts, if the image is smaller than original, it’s reduction. But here image is larger.

Unless... maybe the arrow shows direction? In graph b, there’s an arrow pointing from small to large? Yes — so original is small, image is large → enlargement.

I think the handwritten answer might be wrong. Let me check others.

#### Graph c: Quadrilateral → Image

Original: looks like a diamond shape, distance from center to vertex about 2 units.

Image: same shape, but distance from center to vertex about 1 unit → half size → reduction

Yes — matches handwritten “reducer”

#### Graph d: Two triangles — original and image

Original triangle: base 2 units, height 1 unit

Image triangle: base 4 units, height 2 units → doubled → enlargement

Handwritten says “enlarger” — correct.

So why does graph b say “reducer”? Maybe typo? Or maybe I misidentified original vs image?

Wait — in graph b, is the large rectangle the original? No — typically, the one without prime is original. And in the drawing, the small one is drawn first, then the large one is the result of dilation.

Also, in graph a, small triangle to large triangle → enlargement.

Graph c: large to small → reduction.

Graph d: small to large → enlargement.

So graph b should be enlargement.

But since the student’s sheet has “reducer” written, maybe they made a mistake? Or perhaps the problem defines differently?

Alternatively — maybe in graph b, the dilation is centered elsewhere and it's actually shrinking? Let’s calculate scale factor properly.

Take a point: original bottom-left corner at (1,1). Image bottom-left at (2,2). If center is origin, then vector from origin to (1,1) becomes (2,2) → scale factor 2 → enlargement.

If center were different, say (0,0), still same.

I think it’s safe to say graph b is enlargement, even though handwritten says reducer — probably error.

But to match what’s expected, perhaps we go by visual comparison only.

Another way: count grid squares.

In graph b: original rectangle covers 2x3 = 6 square units.

Image covers 4x6 = 24 square units → area multiplied by 4 → linear scale factor 2 → enlargement.

Definitely enlargement.

I’ll proceed with correct math.

So:

a) enlargement
b) enlargement ← correcting the handwritten note
c) reduction
d) enlargement

But since the user’s image shows “reducer” for b, maybe in their class they consider something else? Unlikely.

Perhaps the arrow indicates the direction of transformation? In graph b, arrow points from small to large — so small is original, large is image → enlargement.

I think we should go with correct mathematical reasoning.

Final decisions:

Problem 1:
a) enlargement
b) reduction
c) enlargement
d) reduction
e) enlargement
f) reduction

Problem 2:
a) enlargement
b) enlargement [despite handwritten "reducer", it's incorrect]
c) reduction
d) enlargement

But to be faithful to common textbook problems, sometimes they trick you — let me re-express.

Wait — in graph b, is the image the small one? No, because the labels: the small rectangle has no primes, large has primes? Actually, in the image provided, for graph b, the small rectangle is labeled with letters like A,B,C,D and the large one with A',B',C',D'? I can't see clearly, but assuming standard notation.

Given ambiguity, and since this is for a student, I'll explain both possibilities but conclude with logic.

Actually, let's assume the figure that is drawn first or without prime is original.

In all graphs, the non-prime is original.

In graph b: non-prime is small rectangle → original is small, image is large → enlargement.

I think it's clear.

So final answers:

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

Final Answer:
Problem 1:
a) enlargement
b) reduction
c) enlargement
d) reduction
e) enlargement
f) reduction

Problem 2:
a) enlargement
b) enlargement
c) reduction
d) enlargement