artcolorful8
Answered

Which sequence of transactions map rectangle A to rectangle B?

A) A dilation centered at the origin followed by a translation.

B) A reflection over the x-axis followed by a dilation and a translation

C) A rotation of 180° about the origin followed by a dilation and a
translation

D) A rotation of 90° about the origin followed by a translation.

Which sequence of transactions map rectangle A to rectangle B? A) A dilation centered at the origin followed by a translation. B) A reflection over the x-axis f class=

Answer :

SaniShahbaz

Answer:

The option B) i.e. a reflection over the x-axis followed by a dilation and a translation is the correction option.

Step-by-step explanation:

Rectangle A with the four vertices.

  • Let 'J' be the first vertex (bottom left) with (2, 2) coordinate location.
  • Let 'K' be the second vertex (bottom right) with (8, 2) coordinate location.
  • Let 'L' be the third vertex (upper left ) with (2, 6) coordinate location.
  • Let 'M' be the fourth vertex (upper right ) with (8, 6) coordinate location.

In other words:

  • J(2, 2)
  • K(8, 2)
  • L(2, 6)
  • M(8, 6)

After reflection across x - axis, the x coordinate remains the same, but the y-coordinate changes its sign.

i.e. (x, y) → (x, -y)

so

  • J(2, 2) → J'(2, -2)
  • K(8, 2) → K'(8, -2)
  • L(2, 6) → L'(2, -6)
  • M(8, 6) → M'(8, -6)

Now, dilate by a scale factor 1/2

The rule of dilation by a scale factor of 1/2 is:

(x, y) → (1/2 x, 1/2 y)

so

J(2, 2)              →         J'(2, -2)              →            J''(1, -1)

K(8, 2)             →          K'(8, -2)             →            K''(4, -1)

L(2, 6)             →          L'(2, -6)              →            L''(1, -3)

M(8, 6)            →         M'(8, -6)              →            M''(4, -3)

Then translation:  (x, y) → (x - 6, y -1 )

J(2, 2)       →         J'(2, -2)       →            J''(1, -1)        →  J'''(-5, -2)

K(8, 2)      →          K'(8, -2)       →            K''(4, -1)      →   K'''( -2, -2)

L(2, 6)      →          L'(2, -6)        →            L''(1, -3)       →   L'''(-5, -4)

M(8, 6)     →         M'(8, -6)        →            M''(4, -3)     →  M''' (-2, -4)

Therefore, the option B) i.e. a reflection over the x-axis followed by a dilation and a translation is the correction option.

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