The point T(
–
1,2) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, T'?
can someone explain what the answer is ??
The answer is 1,-2
The point T(
–
1,2) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, T'?
The point L(3,5) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point, L'?
Well, I must say, performing acrobatics with coordinates is quite a circus act! Let's start with point T(-1,2) and spin it around the origin. To rotate a point 180° clockwise, we simply need to change the sign of both coordinates. So, hold on to your funny hat because T' is going to be at (1, -2)! Ta-da!
To find the coordinates of the resulting point T' after rotating point T (-1, 2) 180° clockwise around the origin, you can apply the rotation formula.
The rotation formula for a 2D point (x, y) rotated θ degrees clockwise around the origin is:
x' = x * cos(θ) + y * sin(θ)
y' = -x * sin(θ) + y * cos(θ)
In this case, the rotation angle (θ) is 180°, and the point T has coordinates (-1, 2).
Let's substitute these values into the rotation formula:
x' = -1 * cos(180°) + 2 * sin(180°)
y' = -(-1) * sin(180°) + 2 * cos(180°)
Now, we need to evaluate the trigonometric functions cos(180°) and sin(180°). In this case, we can use the common values for these angles:
cos(180°) = -1
sin(180°) = 0
Replacing these values into the formulas:
x' = -1 * (-1) + 2 * 0 = 1 + 0 = 1
y' = -(-1) * 0 + 2 * (-1) = 0 + (-2) = -2
Therefore, after rotating point T(-1, 2) 180° clockwise around the origin, the resulting point T' has coordinates T'(1, -2).
Ummh, did you make a sketch?
Or, just visualize that the new point has to be T'(1,-2),
that is, just a reflection in the origin.
btw, rotating 180° clockwise or 180° counter-clockwise would put
you in the same location.