Question

plot the image of d under a dilation about the origin with scale factor of $\frac{4}{3}$. draw

Explanation:

Step1: Find the coordinates of point D

From the graph, the coordinates of point D are \((6,2)\).

Step2: Apply the dilation formula

The formula for dilation about the origin with scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = \frac{4}{3}\), \(x = 6\), \(y=2\).
So, \(kx=\frac{4}{3}\times6 = 8\) and \(ky=\frac{4}{3}\times2=\frac{8}{3}\approx2.67\).

Answer:

The image of point D under the dilation has coordinates \((8,\frac{8}{3})\). Plot this point on the coordinate - plane.