Thread:Tuner King 5/@comment-28838092-20150215234156

Information on how to get speed badges in "Qualitatively defining rigid transformations":

Preserves angle measures and segment lengths:

A reflection followed by another reflection over a different line A reflection followed by a rotation

Each point Z with coordinates (x,y)is mapped to a point Z​′​​ with coordinates (−x,y).

Each point on the coordinate plane moves the same distance in the same direction.

A rotation of 68​∘​​ about the point(5,−280)

Each point A is mapped to a point B such that the perpendicular bisector of segment ​ is the line y=5x−2.

Each point is shifted −2 units in the x direction and 7 units in the y direction.

If C is the circle with center O containing pointV, then we send V to the point W on C so that the measure of ∠VOW is 137​∘​​.

Each point P is reflected over the liney=−x.

Each point P with coordinates (x,y) is mapped to a point P​′​​ with coordinates(x+7,y+4).

Each point on the coordinate plane is rotated θ degrees about the origin.

A translation followed by a rotation

A rotation followed by a translation

Each point J with coordinates (x,y) is mapped to a point J​′​​ with coordinates (y,x).

Each pair of points A and B is mapped to another pair of points A​′​​ and B​′​​ such that quadrilateral AA​′​​B​′​​B is a parallelogram.

Point O maps to itself. Each other point Pmaps to point P​′​​ where the measure of∠POP​′​​ is 82​∘​​ and ∣OP∣=∣OP​′​​∣.

Each point Q with coordinates (x,y) is mapped to a point Q​′​​ with coordinates(−x+2,y).

Each pair of points M and N is mapped to another pair of points M​′​​ and N​′​​ such that quadrilateral MM​′​​N​′​​N is a parallelogram.

Point O maps to itself. Each other point Wmaps to point W​′​​ where the measure of∠WOW​′​​ is 15​∘​​ and ∣OW∣=∣OW​′​​∣.

A rotation followed by another rotation about a different center point A reflection followed by a translation

Each point Q is reflected over the liney=10x.

Each point D with coordinates (x,y) is mapped to a point D​′​​ with coordinates(x+1,y−8).

Preserves all angle measures only:

A dilation followed by another dilation with a different center

A translation followed by a dilation

The x and y coordinates of each point are multiplied by −2.

Point O maps to itself, and each other point P is mapped to a point P​′​​ such that ​ is collinear with ​ and five times as long as ​.

Each point P with coordinates (x,y) is mapped to a point P​′​​ with coordinates(2x,2y).

A reflection followed by a dilation

A dilation followed by a rotation

Each point M with coordinates (x,y) is mapped to a point M​′​​ with coordinates(​3​​x​​,​3​​y​​).

Each point A with coordinates (x,y) is mapped to a point A​′​​ with coordinates (​2​​x​​,​2​​y​​).

Each point T with coordinates (x,y) is mapped to a point T​′​​ with coordinates(3x,3y).

Preserves all segment lengths only:

None of these:

A dilation followed by a vertical stretch

Each point K is mapped to a point K​′​​which is 3 units closer to the origin than K.

Point O maps to itself, and each other point P is mapped to a point P​′​​ such that ​ is collinear with ​ and five units longer than ​.

Each point P with coordinates (x,y) is mapped to a point P​′​​ with coordinates(2x,y).

A translation followed by a horizontal stretch

Each point M with coordinates (x,y) is mapped to a point M​′​​ with coordinates(​3​​x​​,3y).

Each point A with coordinates (x,y) is mapped to a point A​′​​ with coordinates(2x,​2​​y​​).

A horizontal stretch by a factor of 2followed by a vertical stretch by a factor of ​2​​1​​

A reflection followed by a horizontal stretch

Each point P with the coordinates(x,y) is rotated ​4​​x​​ radians about the origin.

Must describe a reflection:

Each point J with coordinates (x,y) is mapped to a point J​′​​ with coordinates (y,x).

Each point W with coordinates (x,y) is mapped to a point W​′​​ with coordinates(x,−y).

Each point Z with coordinates (x,y) is mapped to a pointZ​′​​ with coordinates (−x,y).

Each point J is mapped to a point K such that the perpendicular bisector of segment ​ is the linex=3.

Each point Q with coordinates (x,y) is mapped to a point Q​′​​ with coordinates (−x+2,y).

Does not necessarily describe a reflection:

Cannot describe a reflection:

Each point L with coordinates (x,y) is mapped to a point L​′​​ with coordinates(−y,x).

Each point Z with coordinates (x,y) is mapped to a point Z​′​​ with coordinates(−x,−y).

Each pair of points M and N is mapped to another pair of points M​′​​ and N​′​​ such that ​ and ​ are parallel and have equal lengths.

Must describe a rotation

Point O maps to itself. Each other point M maps to pointM​′​​ where the measure of ∠MOM​′​​ is 10​∘​​ and∣OM∣=∣OM​′​​∣.

Point O maps to itself. For another point V on a circle Ccentered at O, map V to the point W on C so that the measure of ∠VOW is 137​∘​​.

Each point A with coordinates (x,y) is mapped to a point A​′​​ with coordinates (−y,x).

Each point C with coordinates (x,y) is mapped to a point C​′​​ with coordinates (−x,−y).

Does not necessarily describe a rotation

Point O maps to itself. Each other point M maps to pointM​′​​ where the measure of ∠MOM​′​​ is 63​∘​​.

Point D maps to itself, and each other point Emaps to another point E​′​​ such that∣DE∣=∣DE​′​​∣.

Point O maps to itself. Each other point P maps to point P​′​​where the measure of ∠POP​′​​ is 78​∘​​.

Cannot describe a rotation

Each point B with coordinates (x,y) is mapped to a point B​′​​ with coordinates (x,−y).

Must describe a translation

Each point P with coordinates (x,y) is mapped to a point P​′​​ with coordinates (x−5,y+2).

Each point P with coordinates (x,y) is mapped to a point P​′​​ with coordinates (x+3,y−4).

Each point is shifted −2 units in the x-direction and 7 units in the y-direction.

Each pair of points A and B is mapped to another pair of points A​′​​ and B​′​​ such that quadrilateral AA​′​​B​′​​B is a parallelogram.

Does not necessarily describe a translation

Each point P is mapped to a point P​′​​ a distance of 5 units from P.

Each pair of points M and N is mapped to another pair of points M​′​​ and N​′​​ such that ∣MM​′​​∣=∣NN​′​​∣.

Cannot describe a translation

Each point P with coordinates (x,y) is mapped to a point P​′​​ with coordinates(−x+5,−y−2).

Each point P is mapped to a point P​′​​ which is 5 units farther from the origin than P.

Each point P is mapped to a different point P​′​​ which is half as far from the origin as P.

Each pair of points C and D is mapped to another pair of points C​′​​ and D​′​​ such that ​ and ​ are perpendicular and have the same length.

Unicorn = reflection or translation

Penquin = rotation

Q = Reflection or rotation

R = Reflection

M = Translation, Reflection or Rotation

N = Rotation, Translation

Δ = Reflection or Rotation

Γ = Rotation

E = All

F = All

U = All

V = Rotation

X = Reflection or Rotation

Y = Reflection or Translation

S = Reflection

T = Translation 