Which of the following is one of the basic ways to represent three-dimensional space in trigonometry?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
8. Vectors
Geometric Vectors
Multiple Choice
Given the points and , which points are reflections of each other across both axes?
A
and
B
and
C
and
D
and
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Verified step by step guidance1
Understand that reflecting a point across the x-axis changes the sign of the y-coordinate, while reflecting across the y-axis changes the sign of the x-coordinate.
Given a point \((x, y)\), reflection across the x-axis results in \((x, -y)\), and reflection across the y-axis results in \((-x, y)\).
To reflect a point across both axes, apply both reflections: first across one axis, then the other, resulting in \((-x, -y)\).
Apply this to the point \((3, 5)\): reflecting across both axes gives \((-3, -5)\).
Compare the given points to identify which pair matches this transformation; the points \((3, 5)\) and \((-3, -5)\) are reflections of each other across both axes.
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