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A triangle has vertices at B(−3, 0), C(2, −1), D(−1, 2). Which series of transformations would produce an image with vertices B″(4, 1), C″(−1, 0), D″(2, 3)?

A. (x, y) → (x, −y), (x, y) → (x + 1, y + 1)
B. (x, y) → (−x, y), (x, y) → (x + 1, y + 1)
C. (x, y) → (x, −y), (x, y) → (x + 2, y + 2)
D. (x, y) → (−x, y), (x, y) → (x + 2, y + 2)
Thanks!

Respuesta :

Answer:

B. (x, y) → (−x, y), (x, y) → (x + 1, y + 1)

Step-by-step explanation:

Explanation:-

Type of Transformation                       Change to co-ordinate point

Vertical Translation up 'd' units                  ( x, y) → (x , y +d)

Vertical Translation down 'd' units             ( x, y) → (x , y -d)

Horizontal translation left 'c' units              ( x, y) → (x-c , y )

Horizontal translation right 'c' units              ( x, y) → (x +c , y )

Reflection over x -axis                                    ( x, y) → (x  , -y )  

Reflection over y -axis                                    ( x, y) → (-x  , y )  

Given data

A triangle has vertices at B(−3, 0), C(2, −1), D(−1, 2).

a) see above transformation table

i) First  Reflection over y- axis

                 (x, y) → (−x, y)

                ( -3 , 0)  → (3, 0)

Next Horizontal translation right '1' units  and Vertical Translation up '1' units

 (x ,y)  → (x +1 , y+1)

         (3 +1 , 0+1)  

          (4 ,1)      

∴ (-3 ,0) →(4,1)        

b)

  i) First  Reflection over y- axis

                 (x, y) → (−x, y)

                ( 2 , -1)  → (-2, -1)

Next  Horizontal translation right '1' units  and Vertical Translation up '1' units

      (x ,y)  → (x +1 , y+1)

             (-2 +1 , -1+1)  

             (-1 ,0)      

        ∴ ( 2 , -1)  → (-1, 0)  

c)

                             

   i) First  Reflection over y- axis

                (x, y) → (−x, y)

                ( -1 , 2)  → (1, 2)

next  Horizontal translation right '1' units  and Vertical Translation up '1' units

          (x ,y)  → (x +1 , y+1)

        (1, 2)      →  (1 +1 , 2+1)  

                       →     (2 ,3)      

        ∴ ( -1,2)  →  (2 ,3)      

   B(−3, 0), C(2, −1), D(−1, 2) is transformation would produce an image with vertices    B″(4, 1), C″(−1, 0), D″(2, 3)                                  

                       

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