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The smaller triangle is a pre-image of the bigger triangle the center of dilation is (2, -1).

What is the scale factor used to create the dilation?
-2
-1/2
1/2
2

The smaller triangle is a pre-image of the bigger triangle the center of dilation is (2, -1). What is the scale factor used to create the dilation? -2 -1/2 1/2 class=

Answer :

Answer:

-2

Step-by-step explanation:

K12

   By using rule for dilation, scale factor used to create the bigger triangle will be (-2).    

   Coordinates of a point (x, y) dilated by a scale factor 'k' about a point (a, b) is given by,

Coordinates of the image point → [k(x - a) + a, k(y - a) + b]

 From the graph attached,

  • Point of dilation → (2, -1)
  • Vertices of the smaller triangle (preimage) → (-1, -1), (2, 2) and (2, -1)
  • Corresponding vertices of the larger (dilated) triangle → (8, -1), (2, -7) and (2, -1)

By the rule of translation,

Image of vertex (-1, -1) → [k(-1 - 2) + 2, k(-1 + 1) - 1]

                                    → [(-3k + 2), -1]

From the graph attached, image of the point (-1, -1) is (8, -1).

Therefore, (-3k + 2) = 8

                          -3k = 8 - 2

                            k = -2

     Hence, scale factor used to create the larger triangle will be (-2).

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