Question

graph the image of △fgh 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 \(F(-5,3)\), \(G(5,3)\), \(H(-5, - 5)\) from the graph.

Step2: Apply the 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 \((x',y')=(k\cdot x,k\cdot y)\).
For point \(F(-5,3)\):
\(x_F'=2\times(-5)=-10\), \(y_F'=2\times3 = 6\), so \(F'(-10,6)\).
For point \(G(5,3)\):
\(x_G'=2\times5 = 10\), \(y_G'=2\times3=6\), so \(G'(10,6)\).
For point \(H(-5,-5)\):
\(x_H'=2\times(-5)=-10\), \(y_H'=2\times(-5)=-10\), so \(H'(-10,-10)\).

Step3: Graph the new triangle

Plot the points \(F'(-10,6)\), \(G'(10,6)\) and \(H'(-10,-10)\) on the coordinate - plane and connect them to form \(\triangle F'G'H'\).

Answer:

Graph the points \(F'(-10,6)\), \(G'(10,6)\) and \(H'(-10,-10)\) and connect them to get the dilated triangle.