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

Question

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] · Answer 1 · 2022-05-17T02:37:01+03:00

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] · Answer 2 · 2022-05-17T01:29:23+03:00

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)