A segment with endpoint a(3,1) and b(-1,-1) is rotated 90 degrees about its origin what are the new of a and b prime?

Rotating 90° about the origin takes

P:(x,y) -> P':(-y,x)

So, plug in your numbers.

What's the answer ?

Second one

To find the new coordinates of points after rotating them 90 degrees counterclockwise about the origin, we can use the following rotation formula:

x' = x * cos θ - y * sin θ
y' = x * sin θ + y * cos θ

where (x', y') are the new coordinates, (x, y) are the original coordinates, and θ is the angle of rotation.

Let's apply this formula to find the new coordinates of points a(3, 1) and b(-1, -1) after rotating 90 degrees counterclockwise.

For point a(3, 1):

x' = 3 * cos 90° - 1 * sin 90° = 0 - 1 * 1 = -1
y' = 3 * sin 90° + 1 * cos 90° = 3 * 1 + 1 * 0 = 3

So, the new coordinates of a' are (-1, 3).

For point b(-1, -1):

x' = -1 * cos 90° - (-1) * sin 90° = -1 * 0 - (-1) * 1 = 1
y' = -1 * sin 90° + (-1) * cos 90° = -1 * 1 + (-1) * 0 = -1

So, the new coordinates of b' are (1, -1).

Therefore, the new coordinates of a' and b' after rotating the segment 90 degrees counterclockwise about its origin are a'(-1, 3) and b'(1, -1) respectively.