Question

graph the image of rectangle stuv after a translation 12 units down.

Explanation:

Step1: Recall translation rule

A translation 12 units down means subtracting 12 from the y - coordinate of each vertex of the rectangle while keeping the x - coordinate the same.

Step2: Identify original vertices

Let's assume the coordinates of the vertices of rectangle STUV are \(S(x_1,y_1)\), \(T(x_2,y_2)\), \(U(x_3,y_3)\), \(V(x_4,y_4)\). From the graph, if \(S(-6,4)\), \(T(-2,4)\), \(U(-2,6)\), \(V(-6,6)\).

Step3: Calculate new vertices

For \(S\): New \(y\) - coordinate is \(y_1 - 12=4 - 12=-8\), so new \(S\) is \((-6,-8)\).
For \(T\): New \(y\) - coordinate is \(y_2 - 12=4 - 12=-8\), so new \(T\) is \((-2,-8)\).
For \(U\): New \(y\) - coordinate is \(y_3 - 12=6 - 12=-6\), so new \(U\) is \((-2,-6)\).
For \(V\): New \(y\) - coordinate is \(y_4 - 12=6 - 12=-6\), so new \(V\) is \((-6,-6)\).

Step4: Graph new rectangle

Plot the new vertices \((-6,-8)\), \((-2,-8)\), \((-2,-6)\), \((-6,-6)\) on the coordinate - plane and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices \((-6,-8)\), \((-2,-8)\), \((-2,-6)\), \((-6,-6)\) on the given coordinate - plane.