Question

write the coordinates of the vertices after a translation 13 units left and 11 units down.
d((□,□))
e((□,□))
f((□,□))
g((□,□))

Explanation:

Step1: Find original coordinates

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

• \( D \): Looking at the graph, \( D \) is at \( (5, 1) \) (since it's 5 units right on the x - axis and 1 unit up on the y - axis).
• \( E \): \( E \) is at \( (8, 2) \) (8 units right on x, 2 units up on y).
• \( F \): \( F \) is at \( (5, 9) \) (5 units right on x, 9 units up on y).
• \( G \): \( G \) is at \( (3, 2) \) (3 units right on x, 2 units up on y).

Step2: Apply translation rules

The translation rule for a translation of \( h \) units left (which means subtracting \( h \) from the x - coordinate) and \( k \) units down (which means subtracting \( k \) from the y - coordinate) is \( (x,y)\to(x - h,y - k) \). Here, \( h = 13 \) and \( k = 11 \).

For \( D(5,1) \):

\( x'=5 - 13=-8 \)
\( y'=1 - 11=-10 \)
So, \( D'(-8,-10) \)

For \( E(8,2) \):

\( x'=8 - 13=-5 \)
\( y'=2 - 11=-9 \)
So, \( E'(-5,-9) \)

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

\( x'=5 - 13=-8 \)
\( y'=9 - 11=-2 \)
So, \( F'(-8,-2) \)

For \( G(3,2) \):

\( x'=3 - 13=-10 \)
\( y'=2 - 11=-9 \)
So, \( G'(-10,-9) \)

Answer:

\( D'(-8, - 10) \)
\( E'(-5, - 9) \)
\( F'(-8, - 2) \)
\( G'(-10, - 9) \)