Rotations & Translations

90 degrees Clockwise

100

Rotate the point (1, 5) 90 degrees clockwise

(5,-1)

200

Rotate the point (-8, -4) 90 degrees clockwise

(-4, 8)

300

Turn 90 degrees clockwise from origin:

A (2, 9)

B (6, 10)

A' (9, -2)

B' (10, -6)

400

90 degrees clockwise is equivalent to what other turn?

270 the other way; 270 counterclockwise because they're both 90 away from the original position

500

Rotate a point at (5,3) 90 degrees clockwise from (1,-2). What are the prime coordinates?

(6, -6)

90 Counterclockwise

100

Rotate the shape 90 degrees clockwise 

A: (5,4) 

B: (8, 4) 

C: ( 7, 10)

A': (4, -5) 

B': (4, -8) 

C' : (10, -7) 

200

Rotate the point (9, 7) 270 degrees clockwise

(-7, 9) 

300

What is the rule for rotating a shape 270 degrees clockwise

(-y, x) 

x & y change places, change the sign of the first number

400

Rotate the point (-8, 5) 270 degrees clockwise 

(-5, -8) 

500

Why is 90 degrees counterclockwise equivalent to 270 degrees clockwise?

They both transport a figure only 90 degrees away from where it originally was.

180 degrees

100

Rotate the point (5, 6) 180 degrees clockwise

(-5, -6) 

200

Rotate the point (-1, 5) 180 degrees around the origin

(1,-5)

300

Rotate the shape 180 degrees clockwise 

A: (5,4) 

B: (8, 4) 

C: ( 7, 10)

A':(-5,-4) 

B': (-8, -4) 

C': (-7, -10)

400

How many 180 degree turns is 360 degrees?

Two

Because 2 times 180 is 360.

500

If 180 degree turns make the original numbers the opposite of what they were, wouldn't a 360 degree turn make that happen again? For a 360 degree turn, what's the rule? Explain.

For 180 opposite x and y (-x, -y)

For another 180, opposite x and y 

This would change numbers back to what they began as.

Translation

100

X to the right 2

x + 2

200

(6, 7) to the right 2

(8, 7)

300

(5, 12) down 3

(5, 9)

400

(1, 2) right 5 and down 2

(6, 0)

500

(3, 9) -----> (4, 8)

Right 1 and down 1 

(x+1, y-1)

Rules

100

What is the rule for rotating 90 degrees clockwise?

Swap numbers then change the sign of the back #

(x,y) ------>(y,-x)

200

What is the rule for a 90 degrees counterclockwise turn?

Swap numbers then change the sign of the front

(x,y)---------> (-y,x)

300

If we otate the shape 180 degrees clockwise 

A: (5,-4) -----> A' (-5, 4)

B: (8, -4) ----> B' (-8, 4)

C: ( 7, -10)---> C' (-7, 10)

Why

For 180's the signs of both numbers changes

(x,y)----> (-x, -y) 

400

What happens if we move either left or right on a coordinate/Cartesian plane?

Subtract from x for going to the left (x-c)

Add to x for going right (x+c)

500

What happens when traveling up or down on a coordinate/Cartesian plane?

Add to y when going up (y+c)

Subtract from y when going down (y-c)