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

• \( E \): Looking at the grid, the x - coordinate is - 5 (since it's 5 units to the left of the origin) and the y - coordinate is 4. So \( E(-5,4) \)
• \( F \): The x - coordinate is - 5 and the y - coordinate is 9. So \( F(-5,9) \)
• \( G \): The x - coordinate is 1 and the y - coordinate is 9. So \( G(1,9) \)
• \( H \): The x - coordinate is 1 and the y - coordinate is 4. So \( H(1,4) \)

Step2: Apply translation rules

The translation rule for a translation of \( h \) units right and \( k \) units down is \( (x,y)\to(x + h,y - k) \). Here, \( h = 3 \) (3 units right) and \( k=12 \) (12 units down).

For \( E(-5,4) \):

New x - coordinate: \( - 5+3=-2 \)
New y - coordinate: \( 4 - 12=-8 \)
So \( E'(-2,-8) \)

For \( F(-5,9) \):

New x - coordinate: \( - 5 + 3=-2 \)
New y - coordinate: \( 9-12=-3 \)
So \( F'(-2,-3) \)

For \( G(1,9) \):

New x - coordinate: \( 1+3 = 4 \)
New y - coordinate: \( 9-12=-3 \)
So \( G'(4,-3) \)

For \( H(1,4) \):

New x - coordinate: \( 1 + 3=4 \)
New y - coordinate: \( 4-12=-8 \)
So \( H'(4,-8) \)

Answer:

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