Module 19: Coordinates for Space—Exercise 1a & 1b - World Science U

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Module 19: Coordinates for Space—Exercise 1a & 1b

final exam

Module 19: Coordinates for Space—Exercise 1a & 1b

Question 1 of 2

1. Question
Consider the usual $(x,y)$ coordinate system and also the $(x^\prime,y^\prime)$ coordinate system, which is rotated $30^\circ$ counterclockwise relative to the $(x,y)$ coordinate system. Let $P$ be the point $(10,10)$ in $(x,y)$ coordinates. What are the coordinates of $P$ in the $(x^\prime,y^\prime)$ coordinate system?
- 1. $(5 – 5\sqrt{3}, -5 + 5\sqrt{3})$
- 2. $(-5 + 5\sqrt{3}, 5 + 5\sqrt{3})$
- 3. $(5 + 5\sqrt{3}, 5 – 5\sqrt{3})$
- 4. $(5 + 5\sqrt{3}, -5 + 5\sqrt{3})$
Correct

Incorrect
Question 2 of 2

2. Question
Consider the usual $(x,y)$ coordinate system and also the $(x^\prime, y^\prime)$ coordinate system, which is rotated $45^\circ$ counterclockwise relative to the $(x,y)$ coordinate system. Let $Q$ be the point $(10,6)$ in $(x,y)$ coordinates. What are the coordinates of $Q$ in the $(x^\prime,y^\prime)$ coordinate system?
- 1. $(8 \sqrt{2}, -2\sqrt{2})$
- 2. $(2 \sqrt{2}, 4\sqrt{2})$
- 3. $(8 \sqrt{2}, 2\sqrt{2})$
- 4. $(-2 \sqrt{2}, 4\sqrt{2})$
Correct

Incorrect

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