Question

if rectangle abdc is translated horizontoally -1 and vertically +3, which of the following correctly depcits rectangle A' B' D' C?

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

Answer 1

To determine the coordinates of the translated rectangle A'B'C'D', we need to apply the horizontal and vertical translations to each vertex of rectangle ABCD.

The translations given are:
- Horizontal shift: -1 (which means we move left by 1 unit)
- Vertical shift: +3 (which means we move up by 3 units)

Let's apply these translations to each vertex:

1. Vertex A:
\( A = (-5, 4) \)
- New x-coordinate: \( -5 - 1 = -6 \)
- New y-coordinate: \( 4 + 3 = 7 \)
- New position: \( A' = (-6, 7) \)

2. Vertex B:
\( B = (-1, 4) \)
- New x-coordinate: \( -1 - 1 = -2 \)
- New y-coordinate: \( 4 + 3 = 7 \)
- New position: \( B' = (-2, 7) \)

3. Vertex C:
\( C = (-5, 1) \)
- New x-coordinate: \( -5 - 1 = -6 \)
- New y-coordinate: \( 1 + 3 = 4 \)
- New position: \( C' = (-6, 4) \)

4. Vertex D:
\( D = (-1, 1) \)
- New x-coordinate: \( -1 - 1 = -2 \)
- New y-coordinate: \( 1 + 3 = 4 \)
- New position: \( D' = (-2, 4) \)

Now we have the new coordinates:
- \( A' = (-6, 7) \)
- \( B' = (-2, 7) \)
- \( C' = (-6, 4) \)
- \( D' = (-2, 4) \)

Thus, the translated rectangle A'B'C'D' has the following vertices:
- A' = (-6, 7),
- B' = (-2, 7),
- D' = (-2, 4),
- C' = (-6, 4).

You would now look for a depiction of these coordinates on a graph or within a multiple-choice format to find the correct representation of rectangle A'B'D'C'.