Question

write the coordinates of the vertices after a translation 10 units left and 5 units up.

Explanation:

First, we need to determine the original coordinates of the vertices \( P \), \( Q \), and \( R \) from the graph.

Looking at the graph:

• For point \( P \): It is at \( (8, -6) \) (since it is 8 units to the right on the x - axis and 6 units down on the y - axis).
• For point \( Q \): It is at \( (8, 3) \) (8 units to the right on the x - axis and 3 units up on the y - axis).
• For point \( R \): It is at \( (2, -5) \) (2 units to the right on the x - axis and 5 units down on the y - axis).

The rule for a translation of \( h \) units left and \( k \) units up is \( (x,y)\to(x - h,y + k) \). Here, \( h = 10 \) (10 units left) and \( k=5 \) (5 units up).

Step 1: Translate point \( P(8,-6) \)

Using the translation rule \( (x,y)\to(x - 10,y + 5) \)
Substitute \( x = 8 \) and \( y=-6 \) into the rule:
\( x'=8 - 10=-2 \)
\( y'=-6 + 5=-1 \)
So the new coordinates of \( P \) are \( (-2,-1) \)

Step 2: Translate point \( Q(8,3) \)

Using the translation rule \( (x,y)\to(x - 10,y + 5) \)
Substitute \( x = 8 \) and \( y = 3 \) into the rule:
\( x'=8-10=-2 \)
\( y'=3 + 5 = 8 \)
So the new coordinates of \( Q \) are \( (-2,8) \)

Step 3: Translate point \( R(2,-5) \)

Using the translation rule \( (x,y)\to(x - 10,y + 5) \)
Substitute \( x = 2 \) and \( y=-5 \) into the rule:
\( x'=2-10=-8 \)
\( y'=-5 + 5=0 \)
So the new coordinates of \( R \) are \( (-8,0) \)

Answer:

The coordinates of the vertices after translation are \( P(-2,-1) \), \( Q(-2,8) \), \( R(-8,0) \)