Answer:
Option d is correct.
Both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.
Step-by-step explanation:
The rule of 180 degree rotation about the origin is:
![(x, y) \rightarrow (-x , -y)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%20%28-x%20%2C%20-y%29)
Since a Rotation of a point through 180°, about the origin when a point a(h, k) is rotated about the origin through 180° in anticlockwise or clockwise direction.
then, By the rule of 180 degree rotation;
![a(h, k) \rightarrow a'(-h , -k)](https://tex.z-dn.net/?f=a%28h%2C%20k%29%20%5Crightarrow%20a%27%28-h%20%2C%20-k%29)
so, it takes the new position i.e, ![a'(-h , -k)](https://tex.z-dn.net/?f=a%27%28-h%20%2C%20-k%29)
Therefore, both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.