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suppose parallelogram ABCD is dilated using a magnitude of 2 and a center of dilation at (-2,-1). What would be the corresponding ordered pair at point A?

A is (-3,1), B is (-5,-1), C is (-1,-2), and D is (1,0)

(-5,0)
(-1,2)
(-4,3)
(-3,0)

1 answer

To dilate a point from a center of dilation, we follow these steps:

  1. Subtract the coordinates of the center of dilation from the coordinates of the point.
  2. Multiply the result by the scale factor (magnitude of dilation).
  3. Add the coordinates of the center of dilation back to the result.

Given:

  • Point A: (-3, 1)
  • Center of dilation: (-2, -1)
  • Magnitude of dilation: 2

Step 1: Subtract the center of dilation from point A.

\[ (-3 - (-2), 1 - (-1)) = (-3 + 2, 1 + 1) = (-1, 2) \]

Step 2: Multiply by the scale factor (2).

\[ (2 \times -1, 2 \times 2) = (-2, 4) \]

Step 3: Add the center of dilation back.

\[ (-2 + (-2), 4 + (-1)) = (-2 - 2, 4 - 1) = (-4, 3) \]

So, the corresponding ordered pair for point A after dilation is (-4, 3).

Therefore, the correct answer is: (-4, 3).