GSE Geometry Unit 1

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Isometry/Rigid Transformations

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Transformations

27 Terms

1

Isometry/Rigid Transformations

Preserve size and shape

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2

The three isometries

Translation, Rotation, Reflection

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3

Reflection

Mirroring a point or figure across a line

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4

Reflection over y=x

(x,y) →(y,x)

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5

Reflection over y = -x

(x,y) →(-y,-x)

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6

Reflection over y = A

Count right(if +A)/left(if -A) from the pre-points to the line of reflection (A) and count that same number of times over that line again. Y stays the same, x changes

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7

Reflection over x = A

Count up(if +A)/down(if -A) from the pre-points to the line of reflection (A) and count that same number of times over that line again. X stays the same, y changes

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8

Reflect over x-axis

Count up(if +A)/down(if -A) from the pre-points to the x-axis and count that same number over the x-axis. X stays the same, y changes

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9

Reflect over y-axis

Count right(if +A)/left(if -A) from the pre-points to the y-axis and count that same number over the y-axis. Y stays the same, x changes

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10

Reflection Coordinate Notation

(x,y) →(x +/- A, y +/- A)

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11

Reflection Formula Notation

rx-axis, ry-axis, ry=x, ry=-x, rA

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12

Rotation

Turning of a figure over a point on a plane

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13

180 degrees rule

(x,y) →(-x,-y)

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14

90 degrees clockwise/270 degrees counterclockwise rule

(x,y) → (y,-x)

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15

90 degrees counterclockwise/270 degrees clockwise

(x,y) →(-y,x)

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16

Rotation Function notation

Rx, +/- degrees ; x = point of rotation; + degrees = Clockwise, - degrees = Counterclockwise

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17

Translation

Moving a point or figure across the plane

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18

Translate (x,y) → (A, 0)

if +A, move right/add, if -A, move left/subtract; Y doesn’t change because y = 0 in this formula.

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19

Translate (x,y) →(0,B)

if +B, move up/add, if -B, move down/subtract; X doesn’t change because x = 0 in this formula.

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20

Translation Coordinate Notation

(x,y) →(x+/- a, y+/- b)

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21

Translation Function Notation

Ta,b

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22

Dilation

change of size, not shape; NOT ISOMETRY

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23

Scale factor (K)

determines the size change; if K > 1, it’s an enlargement. If K < 1, it’s a reduction. If K = 1, No change

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24

Center of dilation

If you connect the corresponding vertices of the image and pre-image, they will meet at a point.

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25

Dilation Coordinate Notation

(x,y) →[x(a), y(b)]

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26

Dilation Function Notation

Dx/y

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27

Composition

A sum of all translations in a problem or a combination; represented by small oval in the middle of every transformation function present; WORK LEFT TO RIGHT.

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