Question

plot the image of figure abcdefgh after a dilation with scale factor 2. one of the sides has been plotted for you. click below to plot a segment. click a segment to delete it.

Explanation:

Step1: Recall dilation rule

For a dilation with scale - factor \(k = 2\), if a point \((x,y)\) in the original figure is dilated about the origin, the new point \((x',y')\) has coordinates \((x',y')=(k x,k y)=(2x,2y)\).

Step2: Identify vertices of original figure

Let's assume the vertices of the original figure \(ABCDEFGH\) have coordinates \((x_i,y_i)\) for \(i = A,B,\cdots,H\).

Step3: Calculate new coordinates

For each vertex \((x_i,y_i)\) of the original figure, the new vertex \((x_i',y_i')\) after dilation has coordinates \(x_i' = 2x_i\) and \(y_i'=2y_i\).

Step4: Plot new figure

Plot the new vertices \((x_i',y_i')\) on the coordinate - plane and connect them in the same order as the original figure to get the dilated figure.

Answer:

Plot the new figure by doubling the \(x\) and \(y\) coordinates of each vertex of the original figure \(ABCDEFGH\) and then connecting the new vertices.