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

Answer 1

To find the new coordinates of rectangle ABDC after the translation, we need to apply the given transformations: a horizontal translation of -1 (which means we move left by 1 unit) and a vertical translation of +3 (which means we move up by 3 units).

Let’s assume the original coordinates of the rectangle ABDC are:

• A(x1, y1)
• B(x2, y1)
• D(x1, y2)
• C(x2, y2)

After applying the transformations:

• For point A (x1, y1):
  • New A' = A'(x1 - 1, y1 + 3)
• For point B (x2, y1):
  • New B' = B'(x2 - 1, y1 + 3)
• For point D (x1, y2):
  • New D' = D'(x1 - 1, y2 + 3)
• For point C (x2, y2):
  • New C' = C'(x2 - 1, y2 + 3)

In summary, after the translation, the new coordinates will be:

• A' = (x1 - 1, y1 + 3)
• B' = (x2 - 1, y1 + 3)
• D' = (x1 - 1, y2 + 3)
• C' = (x2 - 1, y2 + 3)

To identify which depiction correctly represents rectangle A′B′D′C′, you would need to look for a rectangle that has these transformed coordinates based on your specific original coordinates for ABDC. If you have a visual representation or specific coordinates, please provide those so I can help you identify the correct depiction!

Answer 2

The original coordinates are, A is, (-5,4) B is, (-1,4) C is, (-5,1) D is, (-1,1)

Answer 3

Given the original coordinates of rectangle ABDC:

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

We will translate these points with the transformations: a horizontal translation of -1 (to the left) and a vertical translation of +3 (upward).

Applying the translations:

1. Point A (-5, 4):

   • New A' = (-5 - 1, 4 + 3) = (-6, 7)

2. Point B (-1, 4):

   • New B' = (-1 - 1, 4 + 3) = (-2, 7)

3. Point D (-1, 1):

   • New D' = (-1 - 1, 1 + 3) = (-2, 4)

4. Point C (-5, 1):

   • New C' = (-5 - 1, 1 + 3) = (-6, 4)

New Coordinates of A′B′D′C′:

• A′ = (-6, 7)
• B′ = (-2, 7)
• C′ = (-6, 4)
• D′ = (-2, 4)

Characteristics of Rectangle A'B'D'C':

• The x-coordinates of A' and C' are the same (-6), and the x-coordinates of B' and D' are the same (-2).
• The y-coordinates of A' and B' are the same (7), and the y-coordinates of C' and D' are the same (4).

Conclusion:

So, rectangle A′B′D′C′ will have the vertices:

• A′ (-6, 7)
• B′ (-2, 7)
• C′ (-6, 4)
• D′ (-2, 4)

Look for a visual representation or a description that resembles these points to identify the correct depiction of rectangle A′B′D′C′.