Question

graph the image of \\( \triangle qrs \\) after a translation 5 units right and 7 units down.

Explanation:

Step1: Find the coordinates of original points

Assume \( Q(-10,10) \), \( R(1,10) \), \( S(-9,1) \).

Step2: Apply the translation rule

The translation rule is \( (x,y)\to(x + 5,y-7) \).
For point \( Q(-10,10) \):
\( x=-10+5=-5 \), \( y = 10-7 = 3 \), so \( Q'(-5,3) \).
For point \( R(1,10) \):
\( x=1 + 5=6 \), \( y=10-7 = 3 \), so \( R'(6,3) \).
For point \( S(-9,1) \):
\( x=-9+5=-4 \), \( y=1-7=-6 \), so \( S'(-4,-6) \).

Step3: Graph the new triangle

Plot the points \( Q'(-5,3) \), \( R'(6,3) \), \( S'(-4,-6) \) and connect them to form the image of \(\triangle QRS\) after the translation.

Answer:

Graph the points \( Q'(-5,3) \), \( R'(6,3) \), \( S'(-4,-6) \) and connect them.