Question

write the coordinates of the vertices after a translation 4 units left.

Explanation:

Step1: Find original coordinates

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

• \( S \): \( (2, 0) \)
• \( T \): \( (2, 8) \)
• \( U \): \( (10, 9) \) (assuming the y - coordinate of U is 9 as per the graph, maybe a typo in the initial thought, but looking at the grid, U is at (10,9), V at (10,6))
• \( V \): \( (10, 6) \)

Step2: Apply translation rule

A translation 4 units left means we subtract 4 from the x - coordinate of each vertex (the y - coordinate remains the same). The translation rule for a point \( (x,y) \) after moving \( h \) units left is \( (x - h,y) \), here \( h = 4 \).

For \( S(2,0) \):
New x - coordinate: \( 2-4=-2 \), y - coordinate remains 0. So \( S'=(-2,0) \)

For \( T(2,8) \):
New x - coordinate: \( 2 - 4=-2 \), y - coordinate remains 8. So \( T'=(-2,8) \)

For \( U(10,9) \):
New x - coordinate: \( 10-4 = 6 \), y - coordinate remains 9. So \( U'=(6,9) \)

For \( V(10,6) \):
New x - coordinate: \( 10-4=6 \), y - coordinate remains 6. So \( V'=(6,6) \)

Answer:

The coordinates of the vertices after translation are \( S(-2,0) \), \( T(-2,8) \), \( U(6,9) \), \( V(6,6) \)