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a triangle is drawn on a coordinate plane. dilate the figure with a magnitude of 3 in reference to the origin. what are the coordinates of the new vertices A'B'C

a(-2,-5)
b(0,3)
c(6,-3)

1 answer

To dilate a figure in the coordinate plane with respect to the origin, you multiply each coordinate of the vertices by the magnitude of the dilation. In this case, the magnitude is 3.

Let's apply this to each vertex:

  1. For vertex A (-2, -5): \[ A' = (3 \times -2, 3 \times -5) = (-6, -15) \]

  2. For vertex B (0, 3): \[ B' = (3 \times 0, 3 \times 3) = (0, 9) \]

  3. For vertex C (6, -3): \[ C' = (3 \times 6, 3 \times -3) = (18, -9) \]

Thus, the coordinates of the new vertices after dilation are:

  • A' (-6, -15)
  • B' (0, 9)
  • C' (18, -9)