Question

graph the image of \\( \triangle stu \\) after a translation 2 units right and 6 units down.

Explanation:

Step1: Find the coordinates of original points

Assume the coordinates of \(S\), \(T\), \(U\) are \(S(-1,8)\), \(T(0,8)\), \(U(1,0)\) (based on the graph).

Step2: Apply the translation rule

The translation rule for \(2\) units right (\(x\) - coordinate \(+ 2\)) and \(6\) units down (\(y\) - coordinate \(-6\)).
For point \(S(-1,8)\):
\(x=-1 + 2=1\), \(y = 8-6 = 2\), new coordinate \(S'(1,2)\)
For point \(T(0,8)\):
\(x=0 + 2=2\), \(y = 8-6 = 2\), new coordinate \(T'(2,2)\)
For point \(U(1,0)\):
\(x=1 + 2=3\), \(y=0 - 6=-6\), new coordinate \(U'(3,-6)\)

Step3: Plot the new points

Plot \(S'(1,2)\), \(T'(2,2)\) and \(U'(3,-6)\) on the coordinate - plane and connect them to form \(\triangle S'T'U'\)

Answer:

Plot the points \(S'(1,2)\), \(T'(2,2)\) and \(U'(3,-6)\) and connect them.