Question

write the coordinates of the vertices after a translation 6 units right and 1 unit up.
q(□,□)
r(□,□)
s(□,□)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( Q \), \( R \), and \( S \) from the graph.

• For \( Q \): Looking at the grid, \( Q \) is at \( (-7, -7) \) (since it's 7 units left on the x - axis and 7 units down on the y - axis).
• For \( R \): \( R \) is at \( (2, -7) \) (2 units right on the x - axis and 7 units down on the y - axis).
• For \( S \): \( S \) is at \( (-6, -3) \) (6 units left on the x - axis and 3 units down on the y - axis).

Step2: Apply translation rules

The translation rule for moving 6 units right (which means adding 6 to the x - coordinate) and 1 unit up (which means adding 1 to the y - coordinate) is \( (x,y)\to(x + 6,y + 1) \).

For \( Q' \):

Take the coordinates of \( Q(-7,-7) \).

• New x - coordinate: \( -7+6=-1 \)
• New y - coordinate: \( -7 + 1=-6 \)

So, \( Q'=(-1,-6) \)

For \( R' \):

Take the coordinates of \( R(2,-7) \).

• New x - coordinate: \( 2+6 = 8 \)
• New y - coordinate: \( -7+1=-6 \)

So, \( R'=(8,-6) \)

For \( S' \):

Take the coordinates of \( S(-6,-3) \).

• New x - coordinate: \( -6 + 6=0 \)
• New y - coordinate: \( -3+1=-2 \)

So, \( S'=(0,-2) \)

Answer:

\( Q'(-1, -6) \)
\( R'(8, -6) \)
\( S'(0, -2) \)