Question

figure wxyz is translated 2 units to the right and 3 units down to form figure wxyz. what are the coordinates of the vertices of figure wxyz? label the vertices with the correct ordered pairs? w ( , ), x ( , ), y ( , ), z ( , )

Explanation:

First, we need to determine the original coordinates of the vertices of figure \( WXYZ \) from the graph. Let's assume the original coordinates (by looking at the grid):

• \( W \): Let's say from the grid, \( W \) is at \( (-3, 4) \)
• \( X \): \( X \) is at \( (-1, 4) \)
• \( Y \): \( Y \) is at \( (-2, 1) \)
• \( Z \): \( Z \) is at \( (-4, 3) \)

Now, the translation rule is 2 units to the right (which means add 2 to the \( x \)-coordinate) and 3 units down (which means subtract 3 from the \( y \)-coordinate). The translation rule for a point \( (x, y) \) is \( (x + 2, y - 3) \).

Step 1: Find \( W' \)

Original coordinates of \( W \): \( (-3, 4) \)
Apply translation: \( x' = -3 + 2 = -1 \), \( y' = 4 - 3 = 1 \)
So, \( W' = (-1, 1) \)

Step 2: Find \( X' \)

Original coordinates of \( X \): \( (-1, 4) \)
Apply translation: \( x' = -1 + 2 = 1 \), \( y' = 4 - 3 = 1 \)
So, \( X' = (1, 1) \)

Step 3: Find \( Y' \)

Original coordinates of \( Y \): \( (-2, 1) \)
Apply translation: \( x' = -2 + 2 = 0 \), \( y' = 1 - 3 = -2 \)
So, \( Y' = (0, -2) \)

Step 4: Find \( Z' \)

Original coordinates of \( Z \): \( (-4, 3) \)
Apply translation: \( x' = -4 + 2 = -2 \), \( y' = 3 - 3 = 0 \)
So, \( Z' = (-2, 0) \)

Answer:

\( W'(-1, 1) \)
\( X'(1, 1) \)
\( Y'(0, -2) \)
\( Z'(-2, 0) \)