Question

write the coordinates of the vertices after a translation 11 units left and 1 unit down.

Explanation:

Step1: Identify original coordinates

Let's assume the original coordinates of the vertices are \(S(5,3)\), \(T(7,3)\), \(U(9,7)\), \(V(7,7)\) by observing the graph.

Step2: Apply translation rule for x - coordinate

The translation is 11 units left. The rule for x - coordinate of a point \((x,y)\) after moving left is \(x'=x - 11\).
For \(S\): \(x_S'=5 - 11=-6\); for \(T\): \(x_T'=7 - 11=-4\); for \(U\): \(x_U'=9 - 11=-2\); for \(V\): \(x_V'=7 - 11=-4\).

Step3: Apply translation rule for y - coordinate

The translation is 1 unit down. The rule for y - coordinate of a point \((x,y)\) after moving down is \(y'=y - 1\).
For \(S\): \(y_S'=3 - 1 = 2\); for \(T\): \(y_T'=3 - 1=2\); for \(U\): \(y_U'=7 - 1 = 6\); for \(V\): \(y_V'=7 - 1=6\).

Answer:

\(S'(-6,2)\), \(T'(-4,2)\), \(U'(-2,6)\), \(V'(-4,6)\)