Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
3. Rotations
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Exercise 10 Page 59

Reflect the image across the y-axis to switch from the perspective from the sky to the perspective from the ground.

It says HELLO, rotate it 90^(∘) counterclockwise

Practice makes perfect

Let's take a look at the given diagram. Note that the positive y-axis represents the cardinal direction north.

skytyping from book

This diagram shows how the skytyped message looks from the sky. We want to know what the message says. Also, we want to determine how we should transform the message so that it could be read from north to south. Let's answer these questions one at a time.

What the Message Says

Let's first take a look at how the message could be created.
skytyping from book

Right now, it is hard to read what the message says. After all, this is how the message looks from the sky. Since the viewers are on the ground, the message looks different to them.

Different perspectives

To switch between the perspectives, we need to flip the message across the vertical axis.

Let's see how the message looks for the viewers on the ground.
HELLO
This time we can easily read the message — it says HELLO!

Reading From North to South

Now, we also want to know how we should transform the message so that it is read from north to south. Let's look at the message from the ground again.

The word 'HELLO' formed through plotted points on a coordinate plane
The positive y-axis still represents north. Since we want the message to be read from north to south, we rotate it about the origin by 90^(∘) clockwise.
HELLO rotated clockwise
However, this is how we would see the transformation from the ground. Let's think about how this motion would look from the sky's perspective.
Different perspectives
We can see that a clockwise rotation from the ground's perspective is a counterclockwise rotation from the sky. Because the original diagram is how the message looks from the sky, we have to rotate it counterclockwise by 90^(∘).
HELLO rotated counterclockwise