TCP - Rotations Lesson

Rotations

Rotations are the third type of transformation we will discover! Rotations preserve the shape and size of an object, but do change the orientation.

Let's start with the figure below of John:

graph of John: circle with two points and three line segments

What are the coordinates of John's left eye? (3, 2)

What are the coordinates of John's right eye? (4, 2)

Now, we are going to rotate John about the origin. In this course, we will rotate an object counter-clockwise around the origin.

Graph with description of quadrant locations: Quadrant 1 (upper right) to Quadrant 2 (upper left). Quadrant 3 (bottom left) to Quadrant 4 (bottom right)

180° Rotation

Now, let's try rotating John 180° about the origin.

Graph of 180° rotation counter-clockwise: "John" moves from Quadrant 1 to Quadrant 3 and is upside down

What are the new coordinates of John's left eye? (-3, -2)

What are the new coordinates of John's right eye? (-4, -2)

Using the new coordinates, can you write a rule for rotating a point (x, y) 180° about the origin? (-x, -y)

90° Rotation

So let's see what happens when we rotate John 90°.

Graph of 90° rotation counter clockwise: "John" moves from Quadrant 1 to Quadrant 2 and is on its side

What are the new coordinates of John's left eye? (-2, 3)

What are the new coordinates of John's right eye? (-2, 4)

Using the new coordinates, can you write a rule for rotating a point (x, y) 90° counter-clockwise about the origin? (-y, x)

270° Rotation

So let's see what happens when we rotate John 270°.

Graph of 270° rotation counter clockwise: "John" moves from Quadrant 1 to Quadrant 4 and is its side

What are the new coordinates of John's left eye? (2, -3)

What are the new coordinates of John's right eye? (2, -4)

Using the new coordinates, can you write a rule for rotating a point (x, y) 270° counter-clockwise about the origin? (y, -x)

Let's review the different rules for different rotations:

Rotations Counter-Clockwise Around the Origin
90°	180°	270°
$LaTeX: \left(x,y\right)\longrightarrow\left(-y,x\right)$ $\left(x,y\right)\longrightarrow\left(-y,x\right)$	$LaTeX: \left(x,y\right)\longrightarrow\left(-x,-y\right)$ $\left(x,y\right)\longrightarrow\left(-x,-y\right)$	$LaTeX: \left(x,y\right)\longrightarrow\left(y,-x\right)$ $\left(x,y\right)\longrightarrow\left(y,-x\right)$

Watch this video to try a few more:

Rotations Practice

IMAGES CREATED BY GAVS