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 \( (-3, 5) \) (since moving left -3 on x - axis and up 5 on y - axis)
• \( X \): Let's assume \( X \) is at \( (-1, 5) \)
• \( Y \): Let's assume \( Y \) is at \( (-2, 2) \)
• \( Z \): Let's assume \( Z \) is at \( (-4, 3) \)

Step 1: Recall the translation rule

When a point \( (x,y) \) is translated \( h \) units to the right and \( k \) units down, the new coordinates \( (x',y') \) are given by \( x'=x + h \) and \( y'=y - k \). Here, \( h = 2 \) (right) and \( k = 3 \) (down).

Step 2: Find coordinates of \( W' \)

For \( W(-3,5) \):
\( x'=-3 + 2=-1 \)
\( y'=5-3 = 2 \)
So \( W'(-1,2) \)

Step 3: Find coordinates of \( X' \)

For \( X(-1,5) \):
\( x'=-1 + 2 = 1 \)
\( y'=5-3=2 \)
So \( X'(1,2) \)

Step 4: Find coordinates of \( Y' \)

For \( Y(-2,2) \):
\( x'=-2 + 2=0 \)
\( y'=2-3=-1 \)
So \( Y'(0,-1) \)

Step 5: Find coordinates of \( Z' \)

For \( Z(-4,3) \):
\( x'=-4 + 2=-2 \)
\( y'=3-3 = 0 \)
So \( Z'(-2,0) \)

Answer:

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