Question

graph the image of △stu after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify the coordinates of vertices

Let's assume the coordinates of \(S(-6,5)\), \(T(6,5)\), \(U(-6,1)\) from the graph.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 2\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \(x'=k\times x\) and \(y'=k\times y\).
For point \(S(-6,5)\):
\(x_S'=2\times(-6)= - 12\), \(y_S'=2\times5 = 10\), so \(S'(-12,10)\)
For point \(T(6,5)\):
\(x_T'=2\times6=12\), \(y_T'=2\times5 = 10\), so \(T'(12,10)\)
For point \(U(-6,1)\):
\(x_U'=2\times(-6)=-12\), \(y_U'=2\times1 = 2\), so \(U'(-12,2)\)

Step3: Graph the new triangle

Plot the points \(S'(-12,10)\), \(T'(12,10)\) and \(U'(-12,2)\) on the coordinate - plane and connect them to form \(\triangle S'T'U'\).

Answer:

Graph the points \(S'(-12,10)\), \(T'(12,10)\) and \(U'(-12,2)\) and connect them to get the dilated triangle.