Question

graph the image of rectangle qrst after a translation 7 units right.

Explanation:

Step1: Recall translation rule

For a translation 7 units right, we add 7 to the x - coordinate of each point.

Step2: Identify original points

Let's assume the coordinates of the vertices of rectangle QRST are \(Q(x_Q,y_Q)\), \(R(x_R,y_R)\), \(S(x_S,y_S)\), \(T(x_T,y_T)\). From the graph, if \(Q(- 8,-2)\), \(R(2,-2)\), \(S(2,2)\), \(T(-8,2)\).

Step3: Calculate new coordinates

For point \(Q\): \(x_{Q_{new}}=-8 + 7=-1\), \(y_{Q_{new}}=-2\), so \(Q'(-1,-2)\).
For point \(R\): \(x_{R_{new}}=2 + 7 = 9\), \(y_{R_{new}}=-2\), so \(R'(9,-2)\).
For point \(S\): \(x_{S_{new}}=2+7 = 9\), \(y_{S_{new}}=2\), so \(S'(9,2)\).
For point \(T\): \(x_{T_{new}}=-8 + 7=-1\), \(y_{T_{new}}=2\), so \(T'(-1,2)\).

Step4: Graph new rectangle

Plot the points \(Q'(-1,-2)\), \(R'(9,-2)\), \(S'(9,2)\), \(T'(-1,2)\) and connect them in order to form the new rectangle.

Answer:

Graph the rectangle with vertices \(Q'(-1,-2)\), \(R'(9,-2)\), \(S'(9,2)\), \(T'(-1,2)\) by plotting these points on the coordinate - plane and connecting them in order.