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

The coordinates of the vertices of the image are:

         A''(0,-3) , B''(3,-2) , C''(1,-1)

If the graph or a figure is rotated 180 degree clockwise or anticlockwise then the change in the coordinates of each of the point of the figure is:

      (x,y) → (-x,-y)

Hence, here if ΔABC  is rotated 180° clockwise about the origin then the change in coordinates is:

  A(-3,0) → A'(3,0)

  B(-2,3) → B'(2,-3)

  C(-1,1) → C'(1,-1)

and now when it is reflected across the line y= -x then the change in coordinates or the rule is given by:

       (x,y) → (-y,-x)

Hence, we get:

   A'(3,0) → A''(0,-3)

   B'(2,-3) → B''(3,-2)

and C'(-1,1) → C''(1,-1)

-14 is the answer

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