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

Question

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

Answer 1

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): \[ A' = (-5 - 1, 4 - 3) = (-6, 1) \]

2. Point B (-1, 4): \[ B' = (-1 - 1, 4 - 3) = (-2, 1) \]

3. Point C (-5, 1): \[ C' = (-5 - 1, 1 - 3) = (-6, -2) \]

4. Point D (-1, 1): \[ D' = (-1 - 1, 1 - 3) = (-2, -2) \]

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)