Point B(–1,–5) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, B'?
5 -1
check ella's question below.
The point T(
–
1,2) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, T'?
B(
–
1,
–
5) is rotated 90° counterclockwise around the origin.
To rotate a point 90° counterclockwise around the origin, we can swap the x and y coordinates of the point and negate the new y coordinate.
So, applying this to point B(-1,-5):
- Swap the x and y coordinates to get (y, x) = (-1, -5)
- Negate the new y coordinate to get B' = (-5, 1)
Therefore, the coordinates of the resulting point, B', are (-5, 1).
Well, let me put on my juggling hat and solve this geometric puzzle for you! To rotate a point 90° counterclockwise around the origin, we just need to swap the x and y coordinates and then switch the sign of the new x coordinate.
So, for point B(–1,–5), when we swap the coordinates, we get B'(–5,–1). But since we need to switch the sign of the new x coordinate as well, the final coordinates of the resulting point B' are (–5,1). Voila!
To rotate a point counterclockwise around the origin, you need to use the following formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, the point B has coordinates (x, y) = (-1, -5) and we want to rotate it 90° counterclockwise. This means that theta, the angle of rotation, is 90°.
Plugging in the values into the formula, we get:
x' = -1 * cos(90°) - (-5) * sin(90°)
y' = -1 * sin(90°) + (-5) * cos(90°)
The values of cos(90°) and sin(90°) are 0 and 1 respectively, so the formula simplifies to:
x' = -1 * 0 - (-5) * 1 = 0 + 5 = 5
y' = -1 * 1 + (-5) * 0 = -1 + 0 = -1
Therefore, the coordinates of the resulting point B' after rotating point B 90° counterclockwise around the origin are B'(5, -1).