Transformations on the Coordinate Plane

Transformations on the Coordinate Plane

Transformations

Changing the location, orientation or size of a figure

There are four types of transformations:

• Translation - Moving (Our focus for today)

• Rotation - Turning

• Reflection - Flipping

• Dilation - Changing size

Notations of Translations

• The three ways you can see it written for a problem:

• Words: One to the left, 3 up

• Coordinates: (x, y) -> (x - 1, y + 3)

• Subscript Notation: T_(-1,3)

How to figure out the translation rule:

• Locate the original point (A)

• Locate the new point (A')

• Count the horizontal change (+5)

• Count the vertical change (-3)

• 5 right, 3 down

• (x, y) -> (x + 5, y - 3)

• T_{(5, 3)}

You try some!

3, 2, 1...

Multiple Choice

Click on the image to make it larger. Then determine the transformation that has occurred on this graph.

• A) translation: 2 units left and 5 units down

• B) translation: 1 unit left

• C) translation: 4 units down

• D) translation: 4 units left and 1 unit down

Multiple Choice

Click on the image to make it larger. Then determine the transformation that has occurred on this graph.

• A) translation: 7 units left and 6 units up

• B) translation: 4 units left and 7 units up

• C) translation: 1 unit left and 8 units up

• D) translation: 7 units left and 3 units up

Finding the new point after a translation:

• Graphically:

• Follow the rule on the graph and read the new coordinate values

• Algebraically:

• Right add to x, left subtract from x

• Up add to y, down subtract from y

You try some!

3, 2, 1...

Multiple Choice

Click on the image to make it larger. Then determine the new coordinates of this image under the transformation stated.

• A) D'(−2, 1), E'(0, 2), F'(2, −2)

• B) D'(−1, 4), E'(1, 5), F'(3, 1)

• C) D'(−3, 1), E'(−1, 2), F'(1, −2)

• D) D'(−5, 4), E'(−3, 5), F'(−1, 1)

Multiple Choice

Click on the image to make it larger. Then determine the new coordinates of this image under the transformation stated.

• A) F'(−4, 1), G'(−4, 2), H' (1, 1), I'(−1, −2)

• B) F'(−5, 1), G'(−5, 2 ), H'(0, 1), I'(−2, −2)

• C) F'(0, 4), G'(0, 5), H'(5, 4), I'(3, 1)

• D) F'(−3, 4), G'(−3, 5), H'(2, 4), I'(0, 1)

Independent Practice Time!

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Perform the transformations for each problem on your worksheet, click next to check your answers!

Answers to Questions 11 & 12

Perform the transformations for each problem on your worksheet, click next to check your answers!

Answers to Questions 13 & 14

Perform the transformations for each problem on your worksheet, click next to check your answers!

Answers to Questions 15 & 16

Perform the transformations for each problem on your worksheet and record the coordinates of your new points.

Click next to check your answers!

Answers to Questions 17 & 18

Perform the transformations for each problem on your worksheet and record the coordinates of your new points.

Click next to check your answers!

Answers to Questions 19 & 20

Perform the transformations for each problem on your worksheet and record the coordinates of your new points.

Click next to check your answers!

Answers to Questions 21 & 22

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