Question

write the coordinates of the vertices after a translation 6 units left.
r(□, □)
s(□, □)
t(□, □)
u(□, □)

Explanation:

Step1: Find original coordinates

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

• \( R \): Looking at the graph, \( R \) is at \( (3, -8) \)
• \( S \): \( S \) is at \( (8, -7) \)
• \( T \): \( T \) is at \( (3, -4) \)
• \( U \): \( U \) is at \( (-1, -7) \)

Step2: Apply translation (6 units left)

A translation 6 units left means we subtract 6 from the \( x \)-coordinate of each vertex (since moving left on the \( x \)-axis decreases the \( x \)-value, while the \( y \)-coordinate remains the same).

For \( R(3, -8) \):
New \( x \)-coordinate: \( 3 - 6 = -3 \)
New \( y \)-coordinate: \( -8 \)
So \( R'(-3, -8) \)

For \( S(8, -7) \):
New \( x \)-coordinate: \( 8 - 6 = 2 \)
New \( y \)-coordinate: \( -7 \)
So \( S'(2, -7) \)

For \( T(3, -4) \):
New \( x \)-coordinate: \( 3 - 6 = -3 \)
New \( y \)-coordinate: \( -4 \)
So \( T'(-3, -4) \)

For \( U(-1, -7) \):
New \( x \)-coordinate: \( -1 - 6 = -7 \)
New \( y \)-coordinate: \( -7 \)
So \( U'(-7, -7) \)

Answer:

\( R'(-3, -8) \)
\( S'(2, -7) \)
\( T'(-3, -4) \)
\( U'(-7, -7) \)