Question

write the coordinates of the vertices after a translation 1 unit left 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.

• \( Q \) is at \( (1, -8) \) (since it's 1 unit right on x - axis and 8 units down on y - axis)
• \( R \) is at \( (8, -8) \) (8 units right on x - axis and 8 units down on y - axis)
• \( S \) is at \( (2, -10) \) (2 units right on x - axis and 10 units down on y - axis)

Step2: Apply translation rules

The translation is 1 unit left (subtract 1 from x - coordinate) and 1 unit up (add 1 to y - coordinate). The translation rule is \( (x,y)\to(x - 1,y + 1) \)

For \( Q(1,-8) \):

Substitute \( x = 1 \) and \( y=-8 \) into the translation rule.
\( x'=1 - 1=0 \)
\( y'=-8 + 1=-7 \)
So, \( Q'=(0,-7) \)

For \( R(8,-8) \):

Substitute \( x = 8 \) and \( y = - 8 \) into the translation rule.
\( x'=8-1 = 7 \)
\( y'=-8 + 1=-7 \)
So, \( R'=(7,-7) \)

For \( S(2,-10) \):

Substitute \( x = 2 \) and \( y=-10 \) into the translation rule.
\( x'=2-1 = 1 \)
\( y'=-10 + 1=-9 \)
So, \( S'=(1,-9) \)

Answer:

\( Q'(0, - 7) \)
\( R'(7, - 7) \)
\( S'(1, - 9) \)