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What are the coordinates of the image of parallelogram ABCD after a dilation with center (0, 0) and a scale factor of 3? What are the coordinates of the image of parallelogram ABCD after a dilation with center (0, 0) and a scale factor of 1/2?

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What are the coordinates of the image of parallelogram ABCD after a dilation with center (0, 0) and a scale factor of 3?
What are the coordinates of the image of parallelogram ABCD after a dilation with center (0, 0) and a scale factor of 1/2?




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    1 Answer

    1. Quizzma Team

      To find the coordinates of the image of parallelogram ABCD after dilation, we need to apply the dilation transformation based on the given center and scale factor.

      1. Dilation with a scale factor of 3:

      If the original coordinates of points A, B, C, and D are (x_A, y_A), (x_B, y_B), (x_C, y_C), and (x_D, y_D), respectively, the coordinates of the image after dilation can be calculated using the formula:

      [

      (x’, y’) = (kx, ky)

      ]

      where ( k ) is the scale factor.

      For a scale factor of 3:

      – The new coordinates will be:

      – A’ = (3 * x_A, 3 * y_A)

      – B’ = (3 * x_B, 3 * y_B)

      – C’ = (3 * x_C, 3 * y_C)

      – D’ = (3 * x_D, 3 * y_D)

      2. Dilation with a scale factor of 1/2:

      Similarly, for a scale factor of 1/2, the new coordinates will be:

      – A” = (1/2 * x_A, 1/2 * y_A)

      – B” = (1/2 * x_B, 1/2 * y_B)

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