Answer: The correct option is
(B) (0, -3), (2, -3) and (1, -1).
Step-by-step explanation: Given that the co-ordinates of the vertices of triangle ABC are A (-3,0), B (-2,3), C (-1,1) .
Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.
We are to find the co-ordinates of the vertices of the image.
We know that
if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :
(a, b) ⇒ (-a, -b).
So, after getting rotated 180 degrees clockwise, the co-ordinates of the vertices of triangle ABC becomes
A(-3, 0) ⇒ (3, 0)
B(-2, 3) ⇒ (2, -3)
C(-1, 1) ⇒ (1, -1).
Also, if a point (c, d) i reflected across the line y = -x, hen its co-ordinates changes as follows :
(c, d) ⇒ (-d, -c).
So, after this reflection, the final co-ordiantes of the image of triangle ABC becomes
(3, 0) ⇒ A'(0, -3)
(2, -3) ⇒ B'(3, -2)
(1, -1) ⇒ C'(1, -1).
Thus, the required co-ordinates of the vertices of the image are A'(0, -3), B'(2, -3) and C'(1, -1).
Option (B) is CORRECT.