Answer:
the original position of T before the translation and rotation is (-3,0).
Explanation:
We have the point T(-1,2) and the rotation r(180°, O), where O is the origin.
To find the image of T after the rotation, we need to rotate the coordinates of T by 180° counterclockwise around the origin.
To do this, we can apply the rotation formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Let's substitute the coordinates of T into the formula:
x' = -1 * cos(180°) - 2 * sin(180°)
y' = -1 * sin(180°) + 2 * cos(180°)
Since cos(180°) = -1 and sin(180°)
0, the formulas simplify to:
x' = -1 * (-1) - 2 * (0)
y' = -1 * (0) + 2 * (-1)
Calculating further:
x' = 1
y' = -2
Therefore, the image of T after the rotation r(180°, O) is (1, -2).
T < -1, 2 > ο r(180°, O) : (4, 2)
This statement is incorrect because the image of T after the rotation is not (4, 2), but rather (1, -2).
I hope this explanation helps! Let me know if you have any further questions.