Question

graph the image of parallelogram stuv after a translation 3 units right and 4 units up.

Explanation:

Step1: Recall translation rule

For a translation 3 units right and 4 units up, we add 3 to the x - coordinate and 4 to the y - coordinate of each vertex.

Step2: Identify original vertices

Let's assume the vertices of parallelogram 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 \(S(- 5,-5)\), \(T(0,-5)\), \(U(3,3)\), \(V(-2,3)\).

Step3: Calculate new vertices

For point \(S\): New \(x=-5 + 3=-2\), new \(y=-5 + 4=-1\), so \(S'(-2,-1)\).
For point \(T\): New \(x=0 + 3=3\), new \(y=-5 + 4=-1\), so \(T'(3,-1)\).
For point \(U\): New \(x=3+3 = 6\), new \(y=3 + 4=7\), so \(U'(6,7)\).
For point \(V\): New \(x=-2+3 = 1\), new \(y=3 + 4=7\), so \(V'(1,7)\).

Step4: Graph new parallelogram

Plot the points \(S'(-2,-1)\), \(T'(3,-1)\), \(U'(6,7)\), \(V'(1,7)\) and connect them to form the new parallelogram.

Answer:

Graph the parallelogram with vertices \(S'(-2,-1)\), \(T'(3,-1)\), \(U'(6,7)\), \(V'(1,7)\) on the same coordinate - grid.