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The image below shows a series of transformations that were applied to the triangle ABC, and resulted in the new image.

The image below shows a series of transformations that were applied to the triangle-example-1

1 Answer

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Answer:

The figure is dilated by a scale factor of 1/2 and then translated

A(-6, 8) → A''(3, 2)

The algebraic description that will complete the transformation is:

(x, y) → (x/2 + 6, y/2 - 2)

Explanations:

Let us first consider the coordinates of A, B, and C.

A(-6, 8)

B(-4, 10)

C(-2, 6)

Let us also consider the coordinates of A'', B'', and C''

A''(3, 2)

B''(4, 3)

C''(5, 1)

To know the scale factor for dilation:

A''B'' / AB = 1 / 2 = 0.5

The scale factor for dilation = 2

The coordinates for the vertices, A', B', and C' are therefore:

A'(0.5x-6, 8x0.5) = A' (-3, 4)

B'(0.5x-4, 10x0.5) = B'(-2, 5)

C'(0.5x-2, 6x0.5) = C'(-1, 3)

The triangle A'B'C' was then translated by 6 in the horizontal direction and -2 in the vertical direction.

A''(-3+6, 4-2) = A''(3, 2)

B''(-2+6, 5-2) = B''(4, 3)

C''(-1+6, 3-2) = C''(5, 1)

The figure is dilated by a scale factor of 1/2 and then translated

A(-6, 8) → A''(3, 2)

The algebraic description that will complete the transformation is:

(x, y) → (x/2 + 6, y/2 - 2)

User Vito Valov
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