# American High School Geometry Unit 9: Transformations Project

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Borys_S
School: University of Virginia

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

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.

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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