Transformations on the Coordinate Plane: Rotations - Explains how to rotate figures around the origin using specific angle rules and coordinate mappings.

Let’s solve the problem step by step.

We are told that triangle STU is rotated to become triangle S’T’U’. We’re given coordinates:

Original points:
- S(3, -3) → becomes S’(3, 3)
- T(3, -5) → becomes T’(5, 3)
- U(1, -5) → becomes U’(5, 1)

Wait — let’s double-check the image text. Actually, looking at the “Describing a Rotation” section in the image, it says:

> The signs of both the x-coordinates and y-coordinates changed, which corresponds to the rule for a 180° rotation about the origin: (x, y) → (-x, -y).
> △STU was rotated 180° around the origin.

But wait — let’s verify this with actual numbers from the example shown.

In the image, under “Describing a Rotation”, it shows:

S(3, -3) → S’(3, 3)? That doesn’t match 180° rotation.

Hold on — actually, rereading carefully:

The image says:

> S(3, -3) → S’(3, 3) — but that can’t be right for 180°.

Wait — no! Let me look again.

Actually, in the image, under “Describing a Rotation”, it says:

> S(3, -3) → S’(3, 3) — but then it says “the signs of both x and y changed”.

That contradicts itself unless there’s a typo.

Wait — perhaps I misread. Let me check the actual transformation listed:

It says:

S(3, -3) → S’(3, 3) — that would mean only y changed sign? But then it says “both x and y changed”.

Then it says:

T(3, -5) → T’(5, 3) — that’s not matching any simple rotation.

U(1, -5) → U’(5, 1)

This seems inconsistent.

Wait — perhaps the image has a mistake? Or maybe I’m misreading.

Let me re-express what’s written in the image under “Describing a Rotation”:

It says:

> S(3, -3) → S’(3, 3)
> T(3, -5) → T’(5, 3)
> U(1, -5) → U’(5, 1)

And then it says:

> The signs of both the x-coordinates and y-coordinates changed...

But for S(3,-3) → S’(3,3): x stayed same, y flipped → that’s reflection over x-axis, not 180° rotation.

For T(3,-5) → T’(5,3): x went from 3→5, y from -5→3 — not symmetric.

This doesn’t fit 180° rotation.

Wait — perhaps the image meant to write different coordinates?

Looking back at the image description provided in the user’s upload — actually, the user pasted text that includes:

“S(3, -3) → S’(3, 3)” — but that must be an error because later it says “signs of both changed”.

Alternatively, maybe it’s S(-3, 3) → S’(3, -3)? No.

Wait — let’s read the very last sentence:

> △STU was rotated 180° around the origin.

And the rule for 180° rotation is (x,y) → (-x, -y).

So if original point is (x,y), image should be (-x, -y).

Let’s test with the points as written:

If S(3, -3) → after 180° rotation should be (-3, 3)

But image says S’(3,3) — which is not (-3,3).

Similarly, T(3,-5) → should be (-3,5), but image says T’(5,3)

U(1,-5) → should be (-1,5), but image says U’(5,1)

None of these match 180° rotation.

Unless... perhaps the coordinates are swapped or miswritten?

Wait — maybe the image intended:

S(-3, 3) → S’(3, -3) ? Still not.

Another possibility: maybe it's a 90° clockwise rotation?

Rule for 90° clockwise: (x,y) → (y, -x)

Test S(3,-3) → (-3, -3) — not (3,3)

No.

What about 90° counterclockwise: (x,y) → (-y, x)

S(3,-3) → (3, 3) — oh! That matches S’(3,3)

T(3,-5) → (5, 3) — yes! Because -y = -(-5)=5, x=3 → (5,3)

U(1,-5) → (5, 1) — yes! -y = 5, x=1 → (5,1)

Perfect!

So the rotation is 90° counterclockwise.

But the image says: “The signs of both the x-coordinates and y-coordinates changed, which corresponds to the rule for a 180° rotation...”

That part is incorrect based on the coordinates given.

However, the question is: “Describe the rotation that maps △STU to △S’T’U’.”

Based on the coordinate mappings:

S(3, -3) → S’(3, 3)
T(3, -5) → T’(5, 3)
U(1, -5) → U’(5, 1)

We see:

For each point (x, y) → ( -y , x )

Which is the rule for 90° counterclockwise rotation about the origin.

Confirming with the table in the image:

Under “Counterclockwise Rotations Around the Origin”:

Angle | Rule
90° | (x, y) → (-y, x) ← YES
180° | (x, y) → (-x, -y)
270° | (x, y) → (y, -x)

So our mapping matches 90° CCW.

Therefore, despite the misleading explanation in the image (“signs of both changed”), the actual transformation shown by the coordinates is 90° counterclockwise.

Final Answer:
△STU was rotated 90° counterclockwise around the origin.