Question

Part AWrite functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.translation of a units to the right and b units upreflection across the y-axisreflection across the x-axisrotation of 90 degrees counterclockwise about the origin, point Orotation of 180 degrees counterclockwise about the origin, point Orotation of 270 degrees counterclockwise about the origin, point O

Answer 1

1.

Translation of a units to the right and b units up

According to the rule of translation

let T be the translation then

$T(x,y)=(x+a,y+b)$

2. Reflection across the y axis

According to the rule of reflection across y axis

Let R be the reflection then

$R(x,y)=(-x,y)$

3. Reflection across the x axis

According to the rule of reflection across x axis

Let R be the reflection then

$R(x,y)=(x,-y)$

4. Rotation of 90 degrees counterclockwise about the origin

According to the rule

Let F be the Rotation then

$F(x,y)=(-y,x)$

5.Rotation of 180 degrees counterclockwise about the origin

According to the rule

Let Q be the rotation then

$Q(x,y)=(-x,-y)$

6. Rotation of 270 degrees counterclockwise about the origin

According to the rule

Let P be the rotation then

$P(x,y)=(y,-x)$