Triangle abc with vertices a (-3,0), b (-2,3), c (-1,1) is rotated 180 degrees clockwise about the origin. it is then reflected across the line y=-x. what are the coordinates of the vertices of the image?

 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.

d

step-by-step explanation:

d