Question

graph the image of \\( \triangle t u v \\) after a translation 9 units left and 5 units

Explanation:

Step1: Find the coordinates of \(T\), \(U\), \(V\)

Assume \(T(1,-5)\), \(U(9,-5)\), \(V(1,-3)\)

Step2: Apply the translation rule \((x,y)\to(x - 9,y-5)\)

For point \(T\):
\(x=1,y = - 5\)
\(x'=1-9=-8,y'=-5 - 5=-10\)
New coordinate \(T'(-8,-10)\)
For point \(U\):
\(x = 9,y=-5\)
\(x'=9-9 = 0,y'=-5-5=-10\)
New coordinate \(U'(0,-10)\)
For point \(V\):
\(x = 1,y=-3\)
\(x'=1-9=-8,y'=-3-5=-8\)
New coordinate \(V'(-8,-8)\)

Step3: Plot the new points \(T'(-8,-10)\), \(U'(0,-10)\), \(V'(-8,-8)\) and connect them to form \(\triangle T'U'V'\)

Answer:

Plot the points \(T'(-8,-10)\), \(U'(0,-10)\), \(V'(-8,-8)\) and connect them.