Question

graph the image of \\( \delta t u v \\) after a translation 6 units left and 3 units down.

Explanation:

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

From the graph, \(T(0,5)\), \(U(8,5)\), \(V(-1,6)\)

Step2: Apply the translation rule

The translation rule for \(6\) units left (subtract \(6\) from \(x\)-coordinate) and \(3\) units down (subtract \(3\) from \(y\)-coordinate) is \((x,y)\to(x - 6,y-3)\)

• For point \(T(0,5)\):

\(x=0-6=-6\), \(y = 5-3=2\), so \(T'(-6,2)\)

• For point \(U(8,5)\):

\(x=8 - 6=2\), \(y=5-3 = 2\), so \(U'(2,2)\)

• For point \(V(-1,6)\):

\(x=-1-6=-7\), \(y=6 - 3=3\), so \(V'(-7,3)\)

Step3: Plot the new points and connect them

Plot \(T'(-6,2)\), \(U'(2,2)\), \(V'(-7,3)\) on the coordinate plane and connect them to form \(\triangle T'U'V'\)

Answer:

Plot the points \(T'(-6,2)\), \(U'(2,2)\), \(V'(-7,3)\) and connect them to get the image of \(\triangle TUV\) after the given translation.