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): $$A^{\prime }=(-5-1,4-3)=(-6,1)$$

2. Point B (-1, 4): $$B^{\prime }=(-1-1,4-3)=(-2,1)$$

3. Point C (-5, 1): $$C^{\prime }=(-5-1,1-3)=(-6,-2)$$

4. Point D (-1, 1): $$D^{\prime }=(-1-1,1-3)=(-2,-2)$$

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)