This worksheet helps students practice identifying and applying geometric transformations like translations, reflections, and rotations using coordinate rules.

Let’s solve each transformation problem step by step. We’ll go one at a time, carefully tracking how each point moves.

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1) Rotate 270° about the origin

Rule for 270° rotation (clockwise or counterclockwise? In math, unless specified, we assume counterclockwise).
But note: sometimes worksheets use clockwise — let’s check the example given in #1.

In #1, they show:
Original A(2,3) → New A’(-3,2)

That matches 270° counterclockwise: (x,y) → (-y,x)

Wait — actually, 270° CCW is same as 90° CW.

Standard rules:

- 90° CCW: (x,y) → (-y, x)
- 180°: (x,y) → (-x, -y)
- 270° CCW: (x,y) → (y, -x) ← this matches their example!

Check: A(2,3) → (3, -2)? But they have A’(-3,2). Hmm.

Wait — look again at their table:

They wrote:
A(2,3) → A’(-3,2)

That’s actually 90° counterclockwise: (x,y) → (-y, x) → (2,3) → (-3,2) ✔

But the problem says “Rotate 270° about the origin”.

There’s confusion here. Let me double-check standard conventions.

Actually, many textbooks define:

- 90° CCW: (x,y) → (-y, x)
- 180°: (x,y) → (-x, -y)
- 270° CCW: (x,y) → (y, -x)

But in their example, they rotated 270° and got (-3,2) from (2,3), which is NOT (y,-x)=(3,-2).

Wait — maybe they mean 270° clockwise?

270° clockwise = 90° counterclockwise → (x,y) → (-y,x) → (2,3)→(-3,2) ✔

So likely, in this worksheet, “rotate 270°” means 270° clockwise, which equals 90° CCW.

We’ll follow their pattern.

So rule used in #1: 270° rotation → (x,y) → (-y, x)

Apply to square:

Points: D(1,4), E(2,4), F(2,3), G(1,3)

Apply (x,y) → (-y, x)

D(1,4) → D’(-4,1)
E(2,4) → E’(-4,2)
F(2,3) → F’(-3,2)
G(1,3) → G’(-3,1)

✔ Matches what’s partially filled.

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2) Reflect △JKL across the y-axis

Reflection over y-axis: (x,y) → (-x, y)

Given: J(2,5), K(4,2), L(1,1)

J(2,5) → J’(-2,5)
K(4,2) → K’(-4,2)
L(1,1) → L’(-1,1)

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3) Reflect across the x-axis

Rule: (x,y) → (x, -y)

Points: M(-3,2), N(-1,4), O(-4,5)

M(-3,2) → M’(-3,-2)
N(-1,4) → N’(-1,-4)
O(-4,5) → O’(-4,-5)

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4) Rotate 90° counterclockwise about the origin

Rule: (x,y) → (-y, x)

Points: P(1,2), Q(3,1), R(2,4)

P(1,2) → P’(-2,1)
Q(3,1) → Q’(-1,3)
R(2,4) → R’(-4,2)

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5) Reflect across the y-axis

Same as #2: (x,y) → (-x, y)

Points: S(-2,1), T(-4,3), U(-1,4)

S(-2,1) → S’(2,1)
T(-4,3) → T’(4,3)
U(-1,4) → U’(1,4)

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6) Rotate about the y-axis? Wait — it says “Rotate about the y-axis” but that doesn’t make sense for 2D coordinates. Probably typo.

Looking at the figure: fish shape with points V(1,1), W(3,1), X(2,3)

And the new position is flipped left-right — so likely reflection over y-axis.

Also, in the table, they have original and new columns — probably reflection.

Assume: Reflect across y-axis → (x,y) → (-x,y)

V(1,1) → V’(-1,1)
W(3,1) → W’(-3,1)
X(2,3) → X’(-2,3)

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7) Translate six units up and left 8 units

Translation: move left 8 → subtract 8 from x; up 6 → add 6 to y

Rule: (x,y) → (x-8, y+6)

Points: Y(5,1), Z(7,3), AA(6,5)

Y(5,1) → Y’(5-8,1+6)=(-3,7)
Z(7,3) → Z’(7-8,3+6)=(-1,9)
AA(6,5) → AA’(6-8,5+6)=(-2,11)

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8) Rotate 180° about the origin

Rule: (x,y) → (-x, -y)

Points: BB(2,1), CC(4,3), DD(3,5)

BB(2,1) → BB’(-2,-1)
CC(4,3) → CC’(-4,-3)
DD(3,5) → DD’(-3,-5)

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Now let’s compile all answers neatly.

Final Answer:

1) D’(-4,1), E’(-4,2), F’(-3,2), G’(-3,1)
2) J’(-2,5), K’(-4,2), L’(-1,1)
3) M’(-3,-2), N’(-1,-4), O’(-4,-5)
4) P’(-2,1), Q’(-1,3), R’(-4,2)
5) S’(2,1), T’(4,3), U’(1,4)
6) V’(-1,1), W’(-3,1), X’(-2,3)
7) Y’(-3,7), Z’(-1,9), AA’(-2,11)
8) BB’(-2,-1), CC’(-4,-3), DD’(-3,-5)