Pin on Maths - Free Printable

Let’s go through each graph one by one and figure out what kind of transformation is happening.

We’re looking for three main types:
- Translation – sliding the shape without turning or flipping it.
- Reflection – flipping the shape over a line (like a mirror).
- Rotation – turning the shape around a point.

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Graph 1:
Original triangle ABC → New triangle A’B’C’
Look at where points moved:
A(-3, -4) → A’(2, 0)
B(-2, -1) → B’(3, 3)
C(0, -3) → C’(4, 1)

Each point moved right 5 and up 4. Same direction and distance for all points → Translation

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Graph 2:
Original quadrilateral MNOO’? Wait — actually, looks like polygon M-N-O-O’? Let me check labels.

Actually, original is M-N-O, new is M’-N’-O’. But M and M’ are same point? No — wait, M is at origin, M’ is also at origin? That can’t be.

Wait — let’s read coordinates:

M(0,0), N(2,1), O(2,0)
M’(0,0), N’(4,2), O’(4,0)

So from M to M’: no change
N(2,1) → N’(4,2): right 2, up 1
O(2,0) → O’(4,0): right 2, up 0? Not consistent.

Wait — maybe I misread. Actually, looking again: the figure seems to be stretched? Or scaled?

But transformations in intro usually mean rigid motions: translation, reflection, rotation.

Wait — perhaps it’s a dilation? But the worksheet says “intro to transformations” — often includes only rigid ones.

Wait — look at slopes: MN has slope 1/2, M’N’ has slope 2/4 = 1/2 — same slope. MO is horizontal, M’O’ is horizontal. So angles preserved.

Distance MN: sqrt((2)^2 + (1)^2) = sqrt(5)
M’N’: sqrt((4)^2 + (2)^2) = sqrt(20) = 2*sqrt(5) → doubled.

So this is a dilation (scaling) with center at M (origin), scale factor 2.

But if the worksheet only expects translation/reflection/rotation, maybe they consider this as not covered? But problem says “type of transformation”, and dilation is a transformation.

Looking at other graphs — Graph 6 also looks like dilation.

I think we should include dilation if it fits.

But let’s check instructions: “Determine the type of transformation displayed on each graph.” — doesn’t specify only rigid.

In many curricula, intro transformations include: translation, reflection, rotation, and sometimes dilation.

Given that, Graph 2: all points moved away from origin by factor 2 → Dilation

But wait — M is fixed? M and M’ are both at (0,0). Yes. So center at origin, scale factor 2 → Dilation.

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Graph 3:
P(-3,-3) → P’(3,3)
Q(-1,-1) → Q’(1,1)

Each point (x,y) → (-x,-y)? No: (-3,-3)→(3,3) which is (-x,-y) if x=-3, y=-3 → -x=3, -y=3 → yes.

Actually, (x,y) → (-x,-y) is rotation 180° about origin.

Also could be reflection over origin, but usually called rotation 180°.

Check: vector from origin to P is <-3,-3>, to P’ is <3,3> — exactly opposite → 180° rotation.

→ Rotation (180° about origin)

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Graph 4:
Original ABCD, new A’B’C’D’

A(-4,3) → A’(-4,-3)
B(-2,3) → B’(-2,-3)
C(-1,1) → C’(-1,-1)
D(-3,1) → D’(-3,-1)

All y-coordinates negated, x same → reflected over x-axis.

→ Reflection (over x-axis)

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Graph 5:
D(-3,1) → D’(3,1)
E(-1,3) → E’(1,3)

x-coordinates negated, y same → reflected over y-axis.

→ Reflection (over y-axis)

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Graph 6:
J(-2,0) → J’(-1,0)
K(2,4) → K’(1,2)
L(2,-2) → L’(1,-1)

Each coordinate halved: (x,y) → (x/2, y/2)

Center at origin? J(-2,0)→(-1,0), yes.

Scale factor 1/2 → Dilation (center origin, scale 1/2)

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Graph 7:
This one has arrows showing movement.

A(-4,-4) → A’(-4,4)? Wait, A’ is at (-4,4)? In graph, A’ is top left, A is bottom left.

Actually, looking: A(-4,-4) → A’(-4,4) — that would be reflection over x-axis? But then B(-2,-3) → B’(-2,3)? But in graph, B’ is not directly above.

Wait — let's plot:

Original: A(-4,-4), B(-2,-3), C(-1,-1)
New: A’(-4,4), B’(-2,3), C’(-1,1)

So each (x,y) → (x, -y)? No: (-4,-4)→(-4,4) which is (x, -y) if y=-4, -y=4 → yes.

Similarly, B(-2,-3)→(-2,3) = (x, -y)
C(-1,-1)→(-1,1) = (x, -y)

So reflected over x-axis.

But why arrows? Maybe to show direction, but still reflection.

→ Reflection (over x-axis)

Wait — but in graph 4 we already had reflection over x-axis. This is similar.

But let me confirm positions.

In graph 7, the new figure is above, original below, symmetric over x-axis → yes, reflection over x-axis.

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Graph 8:
Original GHIJ, new G’H’I’J’

G(-2,2) → G’(1,-2)
H(-1,2) → H’(2,-2)
I(-3,0) → I’(0,-4)? Wait, let's get coordinates.

Assume grid: each square 1 unit.

G(-2,2), H(-1,2), I(-3,0), J(0,0) — wait, J is at origin? In graph, J is at (0,0), I at (-3,0)? Let's see:

From graph:
Original: G(-2,2), H(-1,2), I(-3,0), J(0,0) — but J is connected to I and H? Shape is trapezoid.

New: G’(1,-2), H’(2,-2), I’(0,-4), J’(3,-4)? Wait, J’ is at (3,-4)? Let's calculate vectors.

From G to G’: (-2,2) to (1,-2): delta x=+3, delta y=-4
H to H’: (-1,2) to (2,-2): +3, -4
I to I’: (-3,0) to (0,-4): +3, -4
J to J’: (0,0) to (3,-4): +3, -4

All points moved same vector: right 3, down 4 → Translation

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Graph 9:
M(-3,3) → M’(3,3)
N(-1,0) → N’(1,0)
P(-3,-3) → P’(3,-3)

x-coordinates negated, y same → reflected over y-axis.

Also, the lines cross at origin, symmetric.

→ Reflection (over y-axis)

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Now, let's list them:

1. Translation
2. Dilation
3. Rotation (180°)
4. Reflection (x-axis)
5. Reflection (y-axis)
6. Dilation
7. Reflection (x-axis)
8. Translation
9. Reflection (y-axis)

But for graph 2 and 6, if the curriculum doesn't include dilation, what then? But the problem doesn't specify, and visually they are clearly dilations.

In some contexts, "transformation" might imply rigid, but here since sizes change, it must be dilation.

Perhaps for graph 2, it's a combination, but no — it's uniform scaling.

I think it's safe to call them dilations.

Final Answers:

1. Translation
2. Dilation
3. Rotation
4. Reflection
5. Reflection
6. Dilation
7. Reflection
8. Translation
9. Reflection

To be precise, we can specify axes or centers, but the question just says "type", so general terms are fine.

For rotation, we can say "rotation" since 180° is common.

For reflections, sometimes they want the line, but again, "reflection" should suffice.

Looking back at the worksheet title: "Intro to Transformations practice" — likely expects basic types.

In many such worksheets, they accept:

- Slide = translation
- Flip = reflection
- Turn = rotation
- Resize = dilation

So I'll go with that.

Final Answer:

1. Translation
2. Dilation
3. Rotation
4. Reflection
5. Reflection
6. Dilation
7. Reflection
8. Translation
9. Reflection