Question

write the coordinates of the vertices after a translation 8 units right and 2 units down.

(grid with points v, u, s, t plotted; then blanks for s, t, u, v coordinates)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( S \): Looking at the grid, \( S \) is at \( (-4, -6) \)
• \( T \): \( T \) is at \( (0, -5) \)
• \( U \): \( U \) is at \( (-4, -4) \)
• \( V \): \( V \) is at \( (-8, -5) \)

Step2: Apply translation (right 8, down 2)

The translation rule for a point \( (x, y) \) is \( (x + 8, y - 2) \).

For \( S(-4, -6) \):

\( x' = -4 + 8 = 4 \)
\( y' = -6 - 2 = -8 \)
So \( S' = (4, -8) \)

For \( T(0, -5) \):

\( x' = 0 + 8 = 8 \)
\( y' = -5 - 2 = -7 \)
So \( T' = (8, -7) \)

For \( U(-4, -4) \):

\( x' = -4 + 8 = 4 \)
\( y' = -4 - 2 = -6 \)
So \( U' = (4, -6) \)

For \( V(-8, -5) \):

\( x' = -8 + 8 = 0 \)
\( y' = -5 - 2 = -7 \)
So \( V' = (0, -7) \)

Answer:

\( S'(4, -8) \)
\( T'(8, -7) \)
\( U'(4, -6) \)
\( V'(0, -7) \)