Point P(3, 9) in the coordinate plane is rotated 90 degrees counterclockwise about the origin. What are the coordinates of its image?Please show all work and not just the answers.
Answers
Answer:
P'(-9, 3)
Step-by-step explanation:
The transformation for rotation counterclockwise about the origin by some angle α will be ...
(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))
When the angle is α = 90°, this reduces to ...
(x, y) ⇒ (-y, x)
You have (x, y) = (3, 9), so the image point is P'(-9, 3).
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Additional comment
The "work" is applying the right sign and choosing the right coordinate to fill in the values (-y, x). I find it easier to look up the transformations for ±90° and 180°, rather than try to derive them from first principles every time. Your text may have a list:
- 90° CCW or 270° CW: (x, y) ⇒ (-y, x)
- 90° CW or 270° CCW: (x, y) ⇒ (y, -x)
- 180°: (x, y) ⇒ (-x, -y)
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What is the slope of y = 3x + 8?
What is the y-intercept of the equation: y = 4x - 9?
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Need this in 20 min
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Answers
Answer:
slope of y= -1+3x is "3"
of y=-x+7 is "-1"
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9, 10, 6, 5, 6
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Answer: 7.2
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