Transformation Review

Transformation Review

by Victoria Smith

A transformation of a shape is a change in position without changing shape or size.

Transformation

• Reflection - flip

• Rotation - turn

• Translation - slide

​Rotation 90 CCW

Rotating 90 degree counterclockwise (x, y) --> (-y, x). So if (-2, 3), then it would be (-3, -2).

Multiple Choice

If you rotate (1, -3), what is the new coordinate after a 90 degree counterclockwise rotation?

• (-3, 1)

• (1, 3)

• (-1, 3)

• (3, 1)

​Reflecting over y=x

​When you reflect over y = x, the coordinates would flip so

​(x, y) --> (y, x). Example is (2, 3) would become (3, 2).

Multiple Choice

What is the reflection of (-9, 10) over y = x?

• (10, -9)

• (-10, 9)

• (9, -10)

• (9, 10)

​Reflection over y = -x

​When you reflect over y = -x the coordinates flip and change sign so (x, y) --> (-y, -x) for example (-3, -2) becomes (2, 3).

Multiple Choice

What is the coordinate (4, -6) after reflecting over y = -x?

• (-6, 4)

• (6, -4)

• (-4, 6)

• (-4, -6)

​Rotation 270 CCW

​When you rotate 270 degree counterclockwise

​(x, y) --> (y, -x). An example is

​(2, -4) would be (-4, -2).

Multiple Choice

What is (8, 9) after it rotates 270 counterclockwise?

• (9, 8)

• (-9, -8)

• (-9, 8)

• (9, -8)

​Translation

​An object will translate either right or left or up or down.

​(x, y) -- > (x + h, y + k) says to move right h units and up k units.

​(x, y) --> (x - h, y - k) says to move left h units and down k units.

Multiple Choice

What is the new coordinate of (3, -8) after (x, y) --> (x -2, y + 4)?

• (5, -12)

• (1, -4)

• (1, -12)

• (5, -4)

​Rotating 180 degrees.

​When you rotate 180 degrees you can go clockwise or counterclockwise, it will be the same answer.

​(x, y) --> (-x, -y)

​Example (3, 1) becomes (-3, -1)

Multiple Choice

What is (10, 1) after rotating 180 degrees?

• (-10, -1)

• (1, 10)

• (-1, -10)

• (-10, 1)

​Reflecting over the y-axis.

​

​When you reflect over the y-axis the x value will change signs.

​(x, y) -->(-x, y)

​An example is (-2, 1) will become (2, 1).

Multiple Choice

What is (6, -3) after reflecting over y-axis?

• (-6, 3)

• (6, 3)

• (-6, -3)

• (-3, 6)

​Rotating 90 clockwise

​Rotating 90 clockwise is the same as rotating 270 counterclockwise.

​(x, y) -->(y, -x)

​Example (1, 2) becomes (2, -1).

Multiple Choice

Rotate (20, -3) 90 degree clockwise.

• (-3, 20)

• (-3, -20)

• (-20, -3)

• (20, 3)

​Rotate 270 clockwise

​Rotating 270 clockwise is the same as rotating 90 counterclockwise

​(x, y) --> (-y, x) so an example is

​(1, 5) becomes (-5, 1).

Multiple Choice

What is (4, 6) after 270 clockwise rotation?

• (-4, -6)

• (6, 4)

• (-6, -4)

• (-6, 4)

​Reflect over x-axis

​When you reflect over the x-axis, the y value changes sign.

​(x, y) -->(x, -y)

​Example (4, 1) becomes (4, -1)

Multiple Choice

What is (-3, -7) after it reflects over the x-axis?

• (3, -7)

• (-3, 7)

• (3, 7)

• (7, -3)

​What rotation will carry a regular polygon onto itself?

​360/n and its multiples, where n is the number of sides.

​Example: a regular hexagon is 360/6 = 60, 120, 180, 240, 300, 360.

Poll

What is the degree that a regular decagon will carry it onto itself? Select all that apply

• 36

• 72

• 108

• 144

• 180

​I hope you chose all of them! Remember it would be 360/10 = 36, 36 + 36 = 72, 72 + 36 = 108, 108 + 36 = 144, 144 + 36 = 180 and it keeps going until you have 10 different degrees.

​Test tomorrow

​Your test tomorrow and Thursday will consist of pictures and non pictures. There will also be some questions from previous test.

​Central Angle, Exterior Angle of a polygon, Alternate Interior Angles, Alternate Exterior Angles, Consecutive Interior Angles. Study those as well.

​Use quizlet for studying the rules as well and the review angles.