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Ludmilka [50]
3 years ago
8

The point (x,y) is rotated 180 degrees counterclockwise about the origin. Write a rule to determine the coordinate of the image

(x, y). Explain how you found the rule.
Mathematics
2 answers:
ikadub [295]3 years ago
5 0
If a point (x , y) is rotated 180 degrees counter clockwise around the origin, you take the opposites of that point so it now becomes (-x , -y). I hope that helps!!
bazaltina [42]3 years ago
3 0

Answer:

  (x, y) ⇒ (-x, -y)

Step-by-step explanation:

There are a couple of ways you can go at this.

1) Rotation by 180° in either direction is the same as reflection across the origin. That reflection is identical to reflection across both the x- and y-axes, in either order, so negates both coordinates. The transformation rule is ...

  (x, y) ⇒ (-x, -y)

__

2) The rule for a general rotation by angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

For α = 180°, sin(α) = 0 and cos(α) = -1. This makes the rule for rotation by 180° be ...

  (x, y) ⇒ (-x, -y)

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Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the s
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1                4-1=3         2(1)+3=5
2                4-2=2        2(2)+3 = 7
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3 years ago
Could someone help me with this question please!
torisob [31]
X + y = 56 ------------------(1)
x:y = 5:3
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so, x = (5/3)y---------------(2)
sub (2) in (1)
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(5/3)y + y = 56
5 y + 3 y = 168
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x = (5/3) x 21
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