Question

write the coordinates of the vertices after a translation 3 units left.
a((□,□))
b((□,□))
c((□,□))
d((□,□))

Explanation:

Step1: Find original coordinates

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

• \( A(-5, 2) \) (since it's at x = -5, y = 2)
• \( B(1, 2) \) (x = 1, y = 2)
• \( C(2, 10) \) (x = 2, y = 10)
• \( D(-4, 10) \) (x = -4, y = 10)

Step2: Apply translation (3 units left)

A translation 3 units left means subtracting 3 from the x - coordinate (since moving left on the x - axis decreases the x - value), and the y - coordinate remains the same.

For \( A(-5, 2) \):
New x - coordinate: \( -5 - 3=-8 \), y - coordinate remains 2. So \( A'(-8, 2) \)

For \( B(1, 2) \):
New x - coordinate: \( 1 - 3=-2 \), y - coordinate remains 2. So \( B'(-2, 2) \)

For \( C(2, 10) \):
New x - coordinate: \( 2 - 3=-1 \), y - coordinate remains 10. So \( C'(-1, 10) \)

For \( D(-4, 10) \):
New x - coordinate: \( -4 - 3=-7 \), y - coordinate remains 10. So \( D'(-7, 10) \)

Answer:

\( A'(-8, 2) \)
\( B'(-2, 2) \)
\( C'(-1, 10) \)
\( D'(-7, 10) \)