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)

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer: rolling a number cube and flipping a coin.

step-by-step explanation: