Position and Transformation 2

Position and Transformation 2

By Maman Firmansyah

Learning Objectives

​After learning this material, students are able to:

• work out the coordinates of shapes after translation

• reflect shapes in the x-axis or y-axis on a coordinate grid

• rotate shapes 90 degree and 180 degree around the centre of rotationon a coordinate grid

Translating 2D shapes

Multiple Choice

Which letter matches the coordinate (-4, 6)?

• E

• F

• G

• H

Multiple Choice

If you were to plot the point (4, -12) what would be the correct method?

• Up 4, left 12

• Right 4, up 12

• Right 4, down 12

• Down 4, left 12

Multiple Choice

What is the ordered pair of point E?

• (2,5)
• (5,2)
• (-5,2)
• (5,-2)

Open Ended

Write the coordinates of A, B, C, A', B' and C' in the forms of (x,y)!

Open Ended

How do you define the movement from A to A', B to B' and C to C'?

Translating 2D shapes

When you translate a 2D shape on a coordinate grid, you move it right or left and up or down.

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Subject | Subject

Translating 2D shapes

‘ABC is the object’ and that ‘A´B´C´ is the image of ABC´.

Translation is 3 squares right ( + 3 ) and 2 squares up ( + 2 ).

Example 1

A square, ABCD, has vertices at the points A (2, 1), B (5, 2), C (4, 5) and D (1, 4).

ABCD is translated 2 squares right and 1 square down.

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The image of ABCD is A´B´C´D´. Work out the coordinates of the vertices of A´B´C´D´.

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​Solution:

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Subject | Subject

Translating 2D shapes

Multiple Choice

Describe this translation:

• 2 units up

• 2 units down

• 4 units up

• 4 units down

Multiple Choice

The original circle has been translated ___ units to the right.

• 2

• 3

• 4

• 5

Multiple Choice

Where will the point A land when it is translated 2 left and 3 down?

• (9,8)

• (5,2)

• (5,8)

• (9,2)

Multiple Choice

A triangle is translated 2 up and 3 to the left, then 6 down and 5 to the left.

The total translation is ...

• 8 down, 8 left

• 8 down, 8 right

• 4 down, 8 left

• 4 up, 8 right

Reflecting shapes

Triangle A is reflected in the x-axis.

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The x-axis is the horizontal axis. This is the mirror line.

The image of triangle A is labelled triangle B.

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Triangles A and B are congruent.

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Subject | Subject

Reflecting shapes

Example 2

Draw a reflection of this triangle in the y-axis.

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Translating 2D shapes

​Answer:

Multiple Choice

If the letters were reflected in the dotted line, which one would still look the same?

• A

• B

• C

• D

Multiple Choice

Which is true if a point on a coordinate grid is reflected in the y-axis?

• The x coordinate changes sign but the y coordinate doesn’t.

• The y coordinate changes sign but the x coordinate doesn’t.

• Both the x and y coordinates change sign.

Multiple Choice

If the point (4, –1) is reflected in the x-axis, its new coordinates will be:

• (–4, 1)

• (–4, –1)

• (4, 1)

Multiple Choice

The correct reflection of rectangle ABCD in line AB is:

Rotating shapes

When you rotate a shape, you turn it about a fixed point called the centre of rotation.

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You can rotate a shape clockwise or anticlockwise.

You must give the number of degrees by which you are rotating the object.

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Rotating shapes

Example 1

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Rotating shapes

Example 1

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Rotating shapes

Example 1

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Rotating shapes

Example 1

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Rotating shapes

Example 2

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Rotating shapes

Example 2

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Rotating shapes

Example 2

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Rotating shapes

Example 2

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Rotating shapes