contestada

In the same way that other functions can be combined, a series of transformations can be combined into a single function. For example, this statement for the function S shows one way to represent the rotation of a point 270° counterclockwise about the origin followed by a translation 3 units to the left and 1 unit up: S(270, O)/<-3,1>(x, y) = (y – 3, -x + 1).

Write a function to represent each series of transformations:

rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis
reflection across the y-axis, then a translation a units to the right and b units up
translation a units to the right and b units up, then a rotation of 180 degrees counterclockwise about the origin, then a refle

Respuesta :

Answer:

The rotation of 90* reflected across the x-axis, so I would think that it is -O. 90(O,-O).

90(O,-O)greater than or equal to ( a units, b units).

Step-by-step explanation:

The given composite transformations of the point (x, y), gives the

following values;

  • S(90, O)/([tex]Ref_{x-axis}[/tex])(x, ) = (-y, -x)
  • S[tex]\left(Ref_{x-axis})[/tex]/<a, b> (x, y) = (-x + a, y + b)
  • S<a, b>/(180°, 0) = (y + b, x + a)

How can the transformation be expressed as functions?

The given transformations are;

First composite transformation

Rotation 90 degrees counterclockwise about the origin gives;

(x, y) [tex]\underrightarrow{90^{\circ}}[/tex] (-y, x)

A reflection across the x-axis of the point (-y, x) gives (-y - x)

Therefore;

  • S(90, O)/([tex]Ref_{x-axis}[/tex])(x, ) = (-y, -x)

Second composite transformation

Reflection of (x, y) across the y-axis gives (-x, y)

A translation a units to the right and b units up gives (-x + a, y + b)

Which gives;

  • S[tex]\left(Ref_{x-axis})[/tex]/<a, b> (x, y) = (-x + a, y + b)

Third transformation

A translation a units to the right and b units up gives (x + a, y + b)

A rotation 180° counterclockwise of the point (x + a, y + b) gives (y + b, x + a)

Which gives;

  • S<a, b>/(180°, 0) = (y + b, x + a)

Learn more about properties rigid transformations here:

https://brainly.com/question/1801406

Otras preguntas