Question

write the coordinates of the vertices after a translation 3 units right and 12 units down.
e((□,□))
f((□,□))
g((□,□))
h((□,□))

Explanation:

Step1: Find original coordinates

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

• \( E \): Looking at the grid, \( E \) is at \( (-5, 4) \) (since it's 5 units left on the x - axis and 4 units up on the y - axis).
• \( F \): \( F \) is at \( (-5, 9) \) (5 units left on x, 9 units up on y).
• \( G \): \( G \) is at \( (1, 9) \) (1 unit right on x, 9 units up on y).
• \( H \): \( H \) is at \( (1, 4) \) (1 unit right on x, 4 units up on y).

Step2: Apply translation rules

The translation is 3 units right (which means we add 3 to the x - coordinate) and 12 units down (which means we subtract 12 from the y - coordinate). The translation rule for a point \( (x,y) \) is \( (x + 3,y-12) \).

For \( E' \):

Take \( E(-5,4) \). Apply the translation:
\( x'=-5 + 3=-2 \)
\( y'=4-12=-8 \)
So, \( E'(-2,-8) \)

For \( F' \):

Take \( F(-5,9) \). Apply the translation:
\( x'=-5 + 3=-2 \)
\( y'=9-12=-3 \)
So, \( F'(-2,-3) \)

For \( G' \):

Take \( G(1,9) \). Apply the translation:
\( x'=1 + 3=4 \)
\( y'=9-12=-3 \)
So, \( G'(4,-3) \)

For \( H' \):

Take \( H(1,4) \). Apply the translation:
\( x'=1 + 3=4 \)
\( y'=4-12=-8 \)
So, \( H'(4,-8) \)

Answer:

\( E'(-2, - 8) \)
\( F'(-2, - 3) \)
\( G'(4, - 3) \)
\( H'(4, - 8) \)