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Math 10F Transformational Geometry Examples

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Translations Translations are “slides” Described by a length and direction Eg. translate the following shape 6 units left, and 6 units down…

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Translations 6 units left…

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Translations 6 units left… 6 units down

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Translations 6 units left… 6 units down Do the same translation for each key point

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Translations Another example: Translate this shape 5 units left, and 3 units up

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Translations 5 left and 3 up One point

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Translations 5 left and 3 up Two Points

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Translations 5 left and 3 up 3 Points

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Translations 5 left and 3 up All Points (Connect)

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Translations Mapping Notation (x,y) (x+2,y- 4)

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Translations Mapping Notation (x,y) (x+2,y- 4) This means “right 2”, “down 4”

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Translations Mapping Notation (x,y) (x+2,y- 4) This means “right 2”, “down 4” All 4 key points

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Translations Mapping Notation (x,y) (x+2,y- 4) This means “right 2”, “down 4” All 4 key points Connect

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Translations Show the following translations: (x,y) (x+2, y+6) Up 4, left 3 [-4,-1] (ordered pair notation)

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Translations Show the following translations: (x,y) (x+2, y+6) Up 4, left 3 [-4,-1] (ordered pair notation)

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Translations Show the following translations: (x,y) (x+2, y+6) Up 4, left 3 [-4,-1] (ordered pair notation)

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Translations Show the following translations: (x,y) (x+2, y+6) Up 4, left 3 [-4,-1] (ordered pair notation)

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Reflections Reflections are transformations in which a figure is reflected or flipped over a reflection line. Each point in the new figure is the same perpendicular distance from the reflection line as the old point, except on the other side of the line.

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Reflections Reflect the shape through the y-axis.

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Reflections Reflect the shape through the y-axis. Find the perpendicular distances of the key points.

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Reflections Reflect the shape through the y-axis. Find the perpendicular distances of the key points. Find corresponding distances on the other side.

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Reflections Reflect the shape through the y-axis. Find the perpendicular distances of the key points. Find corresponding distances on the other side. Connect the points

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Reflections Reflect the shape through the x-axis.

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Reflections Reflect the shape through the x-axis. Find the perpendicular distances of the key points.

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Reflections Reflect the shape through the x-axis. Find the perpendicular distances of the key points. Find corresponding distances on the other side.

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Reflections Reflect the shape through the x-axis. Find the perpendicular distances of the key points. Find corresponding distances on the other side. Connect the points

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Reflections Reflect the shape through the given reflection line.

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Reflections Reflect the shape through the given reflection line. Find the perpendicular distances of the key points.

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Reflections Reflect the shape through the given reflection line. Find the perpendicular distances of the key points. Find corresponding distances on the other side.

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Reflections Reflect the shape through the given reflection line. Find the perpendicular distances of the key points. Find corresponding distances on the other side. Connect the points

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Rotations A rotation is a transformation in which a figure is turned or rotated about a point. Rotations are CW or CCW All rotations turn relative to the centre of rotation. All rotations in this course will be in 90º increments.

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Rotations Rotate the figure 90º CCW through the origin

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Rotations Rotate the figure 90º CCW through the origin Pick a key point Measure a horizontal distance and a vertical distance to the turn centre

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Rotations Rotate the figure 90º CCW through the origin Pick a key point Measure a horizontal distance and a vertical distance to the turn centre The horizontal distance becomes your new vertical, and your old vertical becomes your new horizontal.

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Rotations Rotate the figure 90º CCW through the origin Do this for EACH key point

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Rotations Rotate the figure 90º CCW through the origin Do this for EACH key point

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Rotations Rotate the figure 90º CCW through the origin Connect the new points to show the rotated figure

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Rotations Rotate the figure 180º CW through the origin

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Rotations Rotate the figure 180º CW through the origin

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Rotations Rotate the figure 90º CW through (0,2)

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Rotations Rotate the figure 90º CW through (0,2)

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Rotations Rotate the figure 90º CW through (3,3)

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Rotations Rotate the figure 90º CW through (3,3)

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Dilations Dilations are enlargements or reductions of a figure The dilation is enlarged by the scale factor (a multiplier) In this class, all dilations will occur about the origin.

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Dilations Dilate the following figure by a scale factor of 3

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Dilations Dilate the following figure by a scale factor of 3

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Dilations Dilate the following figure by a scale factor of 1/2

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Dilations Dilate the following figure by a scale factor of ½ Notice that for dilations, if your scale factor is >1, you are magnifying, and if your SF <1, you are shrinking

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Dilations Dilations can be expressed using a mapping notation Eg. perform the following dilation on the figure given (x,y) (2x,2y)

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Dilations Dilations can be expressed using a mapping notation Eg. perform the following dilation on the figure given (x,y) (2x,2y)

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Dilations For your dilations, the distances from the origin for all key points will be proportional between your two figures

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