*label*Mathematics

### Question Description

This project is based on transformations. (reflection, rotation, etc.) There are three questions in total, please look at the assignment to see if you understand it. While doing the Unit project, make sure that you clearly show all your work and do your best to explain your answers. I will be graded on how well I show my understanding of the concepts as well as correct answers. Show your work if needed, give detailed explanation and solution. You will also be reviewed on how well you show your understanding of the concepts as well as correct answers. this is a graded assignment aim to get 100 A+ thank you.

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## Tutor Answer

The solutions are ready, please ask if something is unclear!docx and pdf files are the same

Task 1. The letters are T, E, S, S, E, L, L, A, T, I, O, N.

The corresponding transformations are:

T

E

S

S

E

L

L

A

T

I

O

N

Reflection over a vertical axis

Reflection over a horizontal axis

Rotation 180 degrees

Rotation 180 degrees

Reflection over a horizontal axis

Reflection over an axis 45 degrees up

Reflection over an axis 45 degrees up

Reflection over a vertical axis

Reflection over a vertical axis

Reflection over a horizontal axis

Reflection over a horizontal axis

Rotation 180 degrees

Task 2.

a. We know 24 hours correspond to 360 degrees, so 2 h 40 min correspond to

2

2+3

8

360° ∙

= 15° ∙ = 𝟒𝟎°.

24

3

b. 𝑃′ lies on the unit circle, so its coordinates are

𝑥 ′ = cos(40°) ≈ 𝟎. 𝟕𝟔𝟔, 𝑦 ′ = sin(40°) ≈ 𝟎. 𝟔𝟒𝟑.

c. To compute it, subtract the coordinates of 𝑃 from the coordinates of 𝑃′ :

cos(40°) − 1 ≈ −0.234, sin(40°) − 0 ≈ 0.643.

This gives the translation about 𝟎. 𝟐𝟑𝟒 units to the left and about 𝟎. 𝟔𝟒𝟑 units up.

Task 3. The picture:

Dilation with center at the origin and scale factor 2 transforms (𝑥, 𝑦) to (2𝑥, 2𝑦).

Because 𝑂(0, 0), 𝑃(1, 3), 𝑀(3, 2), 𝑁(3, 0), the images are 𝑂′ (0, 0)...

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