Given a point on geometric figures (1,2) what is the new point when the point is rotated clockwise about the origin 90 degrees
sorry. (1,2) → (2,-1)
To rotate a point clockwise about the origin, we can use the following rotation formula:
(x', y') = (x * cos(theta) + y * sin(theta), -x * sin(theta) + y * cos(theta))
In this case, the given point is (1, 2), and we want to rotate it clockwise by 90 degrees.
θ = 90 degrees = π/2 radians
Substituting the values into the formula:
(x', y') = (1 * cos(π/2) + 2 * sin(π/2), -1 * sin(π/2) + 2 * cos(π/2))
Evaluate the trigonometric functions:
(x', y') = (1 * 0 + 2 * 1, -1 * 1 + 2 * 0)
= (2, -1)
Therefore, when the point (1, 2) is rotated clockwise by 90 degrees about the origin, the new point is (2, -1).
To find the new point after rotating a point (1,2) clockwise about the origin 90 degrees, we can use the following steps:
1. Plot the original point (1,2) on a coordinate plane.
2. To rotate a point 90 degrees clockwise about the origin, we need to switch the x and y-coordinates of the point and negate the new x-coordinate.
- Switching the x and y-coordinates, we get (2,1).
- Negating the new x-coordinate, we get (-2,1).
3. The new point after rotation is (-2,1).
Here is a visual representation of the steps:
```
Original point (1,2) New Point (-2,1) after
rotation
| |-----------|
| | |
V V | (x-axis)
. . . . . . . . . . . . . . . . .
. * * .
. (1,2) (-2,1) .
. .
. .
```
So, the new point after rotating the original point (1,2) clockwise about the origin 90 degrees is (-2,1).
To rotate a point clockwise about the origin, we use the following rotation formula:
(x', y') = (x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta))
In this case, the given point is (1, 2), and we want to rotate it clockwise by 90 degrees.
θ = 90 degrees = π/2 radians
Substituting the values into the formula:
(x', y') = (1 * cos(π/2) - 2 * sin(π/2), 1 * sin(π/2) + 2 * cos(π/2))
Simplifying:
(x', y') = (1 * 0 - 2 * 1, 1 * 1 + 2 * 0)
= (-2, 1)
Therefore, when the point (1, 2) is rotated clockwise by 90 degrees about the origin, the new point is (-2, 1).