Rotations on a Coordinate Plane

Rotations on a Coordinate Plane

Open Ended

Think back to our last 2 lessons.

1) What does Translation mean in Math?

2) What does Reflection mean in Math?

Open Ended

What does Rotation mean to you?

The shape moves 1 quadrant to the right on the coordinate plane.

90° Clockwise

The shape moves 1 quadrant to the left on the coordinate plane.

​​90° Counter
Clockwise

The shape moves 2 quadrant to the right on the coordinate plane.

180° Clockwise

The shape moves 2 quadrant to the left on the coordinate plane.

180° Counter
Clockwise

Open Ended

What similarities and differences do you notice about the 4 rotations we just talked about?

​Shape rotates 3 quadrants to the right ending up in the same quadrant as a 90° Counter-Clockwise Rotation

​​270° Clockwise → 90⁰ CCW

​Shape rotates 3 quadrants to the leftt ending up in the same quadrant as a 90° Clockwise Rotation

​​270° CCW → 90⁰ Clockwise

​Video clip for next slides, show: 2:16-4:50 question, then on next slide 5:40 to end

Open Ended

What are 3 examples of rotations in the real world?

Multiple Select

Which 2 graphs show a rotation of 180°?

Multiple Select

Which 2 graphs show a rotation of 90° clockwise?

Multiple Select

Which graph shows a rotation of 90° counter-clockwise?

CL-X
x & y switch places
x becomes its opposite
-x → +x
+x → -x

(x, y) → (y, -x)

90° CLockwise

CO-Y
x & y switch places
y becomes its opposite
-y → +y
+y → -y

(x, y) → (-y, x)

90° COunter-clockwise

Algebraic representation Clockwise

x & y stay in their places
both x & y become their opposite
-x → +x
+x → -x
-y → +y
+y → -y
(x, y) → (-x, -y)

180° CLockwise

x & y stay in their places
both x & y become their opposite
-x → +x
+x → -x
-y → +y
+y → -y
(x, y) → (-x, -y)

180° COunter-clockwise

Algebraic representation Clockwise

Switch the directions to 90° Counter-clockwise and use the CL-X rule
x & y switch places
x becomes its opposite
-x → +x
+x → -x
(x, y) → (y, -x)

270° CLockwise

Switch the directions to 90° Clockwise and use the CO-Y rule
x & y switch places
y becomes its opposite
-y → +y
+y → -y
(x, y) → (-y, x)

270° COunter-clockwise

Algebraic representation Clockwise

Multiple Choice

What rotation does the following rule represent?

(x, y) → (-y, x)

• 180° clockwise or counter-clockwise

• 90° Clockwise

• 90° Counter-Clockwise

• 270° Counter-Clockwise

Open Ended

What is the rule for a 180° Clockwise rotation?

Match

Match the following

• 90° Clockwise

• 90° Counter-Clockwise

• 180° Counter-clockwise

• 270° Clockwise

• 270° Counter-Clockwise

(x, y) → (y, -x)

(x, y) → (-y, x)

(x, y) → (-x, -y)

(x, y) → (-y, x)

(x, y) → (y, -x)

• (x, y) → (y, -x)

• (x, y) → (-y, x)

• (x, y) → (-x, -y)

• (x, y) → (-y, x)

• (x, y) → (y, -x)

Multiple Select

What description and rule represents the rotation shown on the graph? (select 2 answers)

• 90° Clockwise

• 90° Counter-Clockwise

• (x, y) → (-y, x)

• (x, y) → (y, -x)

Match

Match the following graphs to the rule that represents the rotation shown

(x, y) → (-x, -y)

(x, y) → (y, -x)

(x, y) → (-y, x)

• (x, y) → (-x, -y)

• (x, y) → (y, -x)

• (x, y) → (-y, x)

Open Ended

Summarize:

1) What is your definition of Rotation?

2) How do the notations help with performing reflections on the coordinate plane?

Multiple Select

Choose the topics you still need help understanding. (You can choose more than 1)

• None. I understand everything in today's lesson

• 
  The difference between image and pre-image.

• Performing rotations using mapping notation

• The definition of a rotations