Question

What are the coordinates of the point obtained by rotating the point (-2, 8) by an angle of 180 degrees?

Answer 1

Answer: (2, -8)

This assumes the center of rotation is the origin (0,0).

The 180 degree rotation rule is
`(\text{x},\text{y}) \to (-\text{x},-\text{y})`

We flip the signs of each coordinate from positive to negative, or vice versa. GeoGebra can be used to verify the answer.

Answer 2

To find the coordinates of a point obtained by rotating another point by an angle of 180 degrees, follow these steps: Subtract 180 degrees from the original angle, convert the polar coordinates to Cartesian coordinates, and calculate the new x and y values.

Step-by-step explanation:

To find the coordinates of a point obtained by rotating another point by an angle of 180 degrees, we can use the following steps:

1. Start with the original point (-2, 8).
2. Apply the rotation by subtracting 180 degrees from the original angle: 180 degrees - 0 degrees = 180 degrees.
3. Use the formula for converting polar coordinates to Cartesian coordinates: x = r*cos(theta) and y = r*sin(theta).
4. Plug in the values r = √((-2)^2 + (8)^2) = √(4 + 64) = √68, and theta = 180 degrees.
5. Calculate x and y:

x = √68 * cos(180) = √68 * (-1) = -8.246

y = √68 * sin(180) = √68 * 0 = 0

Therefore, the coordinates of the point obtained by rotating (-2, 8) by an angle of 180 degrees are (-8.246, 0).