Question

write the coordinates of the vertices after a translation 7 units left.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex. From the graph:

• \( B \): \( (3, 2) \) (since it's 3 units right on x - axis, 2 units up on y - axis)
• \( C \): \( (3, 7) \) (3 units right on x - axis, 7 units up on y - axis)
• \( D \): \( (7, 7) \) (7 units right on x - axis, 7 units up on y - axis)
• \( E \): \( (7, 2) \) (7 units right on x - axis, 2 units up on y - axis)

Step2: Apply translation (7 units left)

A translation 7 units left means we subtract 7 from the x - coordinate of each point (the y - coordinate remains the same). The formula for a translation \( h \) units left is \( (x - h,y) \), where \( h = 7 \).

For point \( B(3,2) \):
New \( x \)-coordinate: \( 3-7=-4 \), \( y \)-coordinate remains 2. So \( B'(-4,2) \)

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

For point \( D(7,7) \):
New \( x \)-coordinate: \( 7-7 = 0 \), \( y \)-coordinate remains 7. So \( D'(0,7) \)

For point \( E(7,2) \):
New \( x \)-coordinate: \( 7 - 7=0 \), \( y \)-coordinate remains 2. So \( E'(0,2) \)

Answer:

The coordinates of the vertices after translation 7 units left are \( B'(-4,2) \), \( C'(-4,7) \), \( D'(0,7) \), \( E'(0,2) \)