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Part A
Write functions for each of the following transformations of the point [tex]\((x, y)\)[/tex] using function notation. Use [tex]\(T\)[/tex] to represent translation, [tex]\(R\)[/tex] to represent rotation, and [tex]\(F\)[/tex] to represent reflection.

Question 1

Write a function to represent the point [tex]\((x, y)\)[/tex] being translated 3 units to the right and 2 units down.
Type the correct answer in the box.
[tex]\[T(x, y) = \][/tex]

Question 2

Write a function to represent the point [tex]\((x, y)\)[/tex] being rotated 90 degrees clockwise about the origin.
Type the correct answer in the box.
[tex]\[R(x, y) = \][/tex]

Question 3

Write a function to represent the point [tex]\((x, y)\)[/tex] being reflected over the y-axis.
Type the correct answer in the box.
[tex]\[F(x, y) = \][/tex]



Answer :

GinnyAnswer
Alright, students! Let's go through the first part of the question step by step.

### Question 1

Translate the point [tex]\((x, y)\)[/tex] by 3 units to the right and 2 units down. We need to write the function [tex]\(T(x, y)\)[/tex] to reflect this transformation.

#### Step 1: Translation to the right

To translate a point [tex]\(x\)[/tex] units to the right, we add to the [tex]\(x\)[/tex]-coordinate. Here, we need to translate 3 units to the right, so we add 3 to the [tex]\(x\)[/tex]-coordinate:

[tex]\[ x' = x + 3 \][/tex]

#### Step 2: Translation downward

To translate a point [tex]\(y\)[/tex] units down, we subtract from the [tex]\(y\)[/tex]-coordinate. Here, we need to translate 2 units down, so we subtract 2 from the [tex]\(y\)[/tex]-coordinate:

[tex]\[ y' = y - 2 \][/tex]

#### Combining Steps 1 and 2

The new coordinates [tex]\((x', y')\)[/tex] after the translation will be:

[tex]\[ (x', y') = (x + 3, y - 2) \][/tex]

Therefore, the function [tex]\(T\)[/tex] that represents this translation is given by:

[tex]\[ T(x, y) = (x + 3, y - 2) \][/tex]

So, the answer is:
[tex]\[ T(x, y) = (x + 3, y - 2) \][/tex]

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