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Given the preimage points: find the coordinates

of the dilated image using the scale factors. *look at picture*

Given the preimage points: find the coordinates of the dilated image using the scale-example-1

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Question 1)

Answer:

Please see the explanation.

Explanation:

We know that the dilation of an original object shows how much bigger or smaller the image will really get, as compared to the original shape.

Also,

  • if the value of scale factor > 1, the image will get bigger.
  • if the value of scale factor < 1, the image will get smaller.

The new coordinates of the image can be determined by multiplying the scale factor with the coordinates of the original object.

Given the preimage points:

  • A(0, 5)
  • B(4, 9)
  • C(-1, -8)

The formula of the dilation by a scale factor of 3:

(x, y) → (3x, 3y)

  • As the scale factor > 1, so the image will be bigger.

Therefore, the coordinates of the dilated image after the dilation by a scale factor of 3 will be:

A(x, y) → (3x, 3y) = A(0, 5) → (3(0), 3(5)) = A'(0, 15)

B(x, y) → (3x, 3y) = B(4, 9) → (3(4), 3(9)) = B'(12, 27)

C(x, y) → (3x, 3y) = C(-1, -8) → (3(-1), 3(-8)) = C'(-3, -24)

Question 2)

Answer:

Please see the explanation.

Explanation:

Given the preimage points:

  • A(0, 5)
  • B(4, 9)
  • C(-1, -8)

The formula of the dilation by a scale factor of 1/2:

(x, y) → (1/2x, 1/2y)

  • As the scale factor < 1, so the image will be smaller.

Therefore, the coordinates of the dilated image after the dilation by a scale factor of 1/2 will be:

A(x, y) → (3x, 3y) = A(0, 5) → (1/2(0), 1/2(5)) = A'(0, 5/2)

B(x, y) → (3x, 3y) = B(4, 9) → (1/2(4), 1/2(9)) = B'(2, 9/2)

C(x, y) → (3x, 3y) = C(-1, -8) → (1/2(-1), 1/2(-8)) = C'(-1/2, -4)

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