If rectangle ABDC is translated horizontally by −1 and vertically by −3 , which of the following correctly depicts rectangle A′B′D′C′?

A = (-5, 4), B = (-1, 4), C = (-5, 1), D = (-1, 1)

1 answer

To translate rectangle ABDC, we need to apply the transformations to each of its vertices:

  • The translation by 1 in the horizontal direction means we subtract 1 from the x-coordinates of each point.
  • The translation by 3 in the vertical direction means we subtract 3 from the y-coordinates of each point.

Now, we will apply these translations to each vertex:

  1. Point A (-5, 4): A=(51,43)=(6,1)

  2. Point B (-1, 4): B=(11,43)=(2,1)

  3. Point C (-5, 1): C=(51,13)=(6,2)

  4. Point D (-1, 1): D=(11,13)=(2,2)

After applying the translations, the new vertices of rectangle A′B′D′C′ are:

  • A′ = (6,1)
  • B′ = (2,1)
  • C′ = (6,2)
  • D′ = (2,2)

Thus, the coordinates of rectangle A′B′D′C′ are:

  • A' = (-6, 1)
  • B' = (-2, 1)
  • C' = (-6, -2)
  • D' = (-2, -2)