Question

write the coordinates of the vertices after a translation 8 units down.
b(( ), ( ))
c(( ), ( ))
d(( ), ( ))
e(( ), ( ))

Explanation:

Step1: Find original coordinates

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

• \( B \): Looking at the grid, \( B \) is at \( (-7, 5) \) (x = -7, y = 5)
• \( C \): \( C \) is at \( (3, 5) \) (x = 3, y = 5)
• \( D \): \( D \) is at \( (3, 7) \) (x = 3, y = 7)
• \( E \): \( E \) is at \( (-7, 7) \) (x = -7, y = 7)

Step2: Apply translation (8 units down)

A translation 8 units down means we subtract 8 from the y - coordinate of each point (the x - coordinate remains the same). The translation rule for a vertical translation down by \( k \) units is \( (x,y)\to(x,y - k) \), here \( k = 8 \).

• For \( B(-7,5) \):

New y - coordinate: \( 5-8=-3 \), so \( B'(-7,-3) \)

• For \( C(3,5) \):

New y - coordinate: \( 5 - 8=-3 \), so \( C'(3,-3) \)

• For \( D(3,7) \):

New y - coordinate: \( 7-8 = - 1\), so \( D'(3,-1) \)

• For \( E(-7,7) \):

New y - coordinate: \( 7-8=-1 \), so \( E'(-7,-1) \)

Answer:

\( B'(-7, -3) \)
\( C'(3, -3) \)
\( D'(3, -1) \)
\( E'(-7, -1) \)