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To draw the image of a figure under a dilation with center M and the scale factor k, we need to follow a few steps.
Notice that M is one of the vertices of the original figure. Therefore, the image and the preimage are the same point M. We will begin by drawing the rays from M through each vertex. Let's also name the remaining vertices A, B, and C.
The given scale factor is k= 2. Let's locate A' on MA such that MA' = 2 MA. To do this, we measure MA first. Then, after multiplying MA by 2, we get the length of MA'. We locate point A' by measuring this length from M along MA.
We can locate B' on MB and C' on MC in the same way we located A' in Step 2.
Finally, we can connect the new vertices and get the image of the original figure.