Rotation of 3 Vertices around the Origin Starting in Quadrant I (A) - Free Printable

To solve these rotation problems, we need to move each corner (vertex) of the shape according to the rules for rotating around the center point $(0,0)$.

Here are the rules we will use:
* Rotate $90^\circ$ Clockwise: A point at $(x, y)$ moves to $(y, -x)$.
* *Simple trick:* Swap the numbers and make the new second number negative.
* Rotate $90^\circ$ Counterclockwise: A point at $(x, y)$ moves to $(-y, x)$.
* *Simple trick:* Swap the numbers and make the new first number negative.

Let's solve each problem one by one.

Problem 1: Top Left

Instruction: Rotate $90^\circ$ clockwise about $(0, 0)$.

1. Identify the points: Looking at the grid, the triangle has corners at:
* Point A: $(1, 4)$
* Point B: $(4, 4)$
* Point C: $(4, 2)$

2. Apply the rule $(x, y) \rightarrow (y, -x)$:
* Point A $(1, 4)$ becomes $(4, -1)$.
* Point B $(4, 4)$ becomes $(4, -4)$.
* Point C $(4, 2)$ becomes $(2, -4)$.

3. Draw: Plot these new points in Quadrant IV (bottom right) and connect them.

Problem 2: Top Right

Instruction: Rotate $90^\circ$ clockwise about $(0, 0)$.

1. Identify the points: The triangle has corners at:
* Point A: $(1, 1)$
* Point B: $(3, 1)$
* Point C: $(3, 5)$

2. Apply the rule $(x, y) \rightarrow (y, -x)$:
* Point A $(1, 1)$ becomes $(1, -1)$.
* Point B $(3, 1)$ becomes $(1, -3)$.
* Point C $(3, 5)$ becomes $(5, -3)$.

3. Draw: Plot these new points in Quadrant IV (bottom right) and connect them.

Problem 3: Bottom Left

Instruction: Rotate $90^\circ$ clockwise about $(0, 0)$.

1. Identify the points: The triangle has corners at:
* Point A: $(1, 3)$
* Point B: $(4, 2)$
* Point C: $(5, 3)$

2. Apply the rule $(x, y) \rightarrow (y, -x)$:
* Point A $(1, 3)$ becomes $(3, -1)$.
* Point B $(4, 2)$ becomes $(2, -4)$.
* Point C $(5, 3)$ becomes $(3, -5)$.

3. Draw: Plot these new points in Quadrant IV (bottom right) and connect them.

Problem 4: Bottom Right

Instruction: Rotate $90^\circ$ counterclockwise about $(0, 0)$.
*(Note: This direction is different from the others!)*

1. Identify the points: The triangle has corners at:
* Point A: $(1, -1)$
* Point B: $(3, -1)$
* Point C: $(3, -3)$

2. Apply the rule $(x, y) \rightarrow (-y, x)$:
* Point A $(1, -1)$: The $y$ is $-1$, so $-y$ is $1$. New point is $(1, 1)$.
* Point B $(3, -1)$: The $y$ is $-1$, so $-y$ is $1$. New point is $(1, 3)$.
* Point C $(3, -3)$: The $y$ is $-3$, so $-y$ is $3$. New point is $(3, 3)$.

3. Draw: Plot these new points in Quadrant I (top right) and connect them.

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Final Answer:
Here are the coordinates for the rotated images you need to draw:

1. Top Left Image (Rotated $90^\circ$ Clockwise):
* Draw a triangle connecting: $(4, -1)$, $(4, -4)$, and $(2, -4)$.

2. Top Right Image (Rotated $90^\circ$ Clockwise):
* Draw a triangle connecting: $(1, -1)$, $(1, -3)$, and $(5, -3)$.

3. Bottom Left Image (Rotated $90^\circ$ Clockwise):
* Draw a triangle connecting: $(3, -1)$, $(2, -4)$, and $(3, -5)$.

4. Bottom Right Image (Rotated $90^\circ$ Counterclockwise):
* Draw a triangle connecting: $(1, 1)$, $(1, 3)$, and $(3, 3)$.