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Dilate the figure by a scale factor 1/2 of with the origin as the center of Gilation. What are the coordinates of the image ABC?

Dilate The Figure By A Scale Factor 12 Of With The Origin As The Center Of Gilation What Are The Coordinates Of The Image ABC class=

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Answer:

The coordinates of the image ABC will be:

  • A'(3, 3)
  • B'(6, 6)
  • C'(15, 12)

Step-by-step explanation:

Given the vertices of an original triangle

  • A(6, 6)
  • B(12, 12)
  • C(30, 24)

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

If the scale factor > 1, the image is enlarged

If the scale factor is between 0 and 1, it gets shrunk

If the scale factor = 1, the object and the image are congruent

Rule to calculate the dilation by a scale factor 1/2 centered at the origin

P(x, y) → P'(1/2x, 1/2y)

so

A(6, 6) → A'(1/2(6), 1/2(6))  → A'(3, 3)

B(12, 12) → B'(1/2(12), 1/2(12))  → B'(6, 6)

C(30, 24) → C'(1/2(30), 1/2(24))  → C'(15, 12)

Therefore, the coordinates of the image ABC will be:

  • A'(3, 3)
  • B'(6, 6)
  • C'(15, 12)
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