Question

find the image based on the graph of the pre - image. dilation of 2.5 about the origin 20. find f

Explanation:

Step1: Recall dilation rule

For a dilation of scale - factor \(k\) about the origin, if a point has coordinates \((x,y)\), its image has coordinates \((kx,ky)\). Here \(k = 2.5\).

Step2: Assume coordinates of point \(F\)

Let's assume the coordinates of point \(F\) are \((x_F,y_F)\). From the graph, if we assume \(F=(1,2)\) (by observing the grid - position).

Step3: Calculate coordinates of \(F'\)

Using the dilation formula \((x',y')=(kx,ky)\), with \(k = 2.5\), \(x_F = 1\) and \(y_F = 2\), we get \(x'_F=2.5\times1 = 2.5\) and \(y'_F=2.5\times2=5\). So the coordinates of \(F'\) are \((2.5,5)\).

Answer:

\((2.5,5)\)