McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
6. Dilations
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Exercise 2 Page 677

Begin by drawing rays from M through each vertex.

Practice makes perfect

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.

  • Step 1: Draw rays from M through each vertex.
  • Step 2: Choose one vertex, which we will arbitrarily call A. Locate A' on MA such that MA' = k MA.
  • Step 3: Repeat Step 2 for the remaining vertices. Then connect the new vertices to create the image.
Let's draw the dilation of the given figure!

Step 1

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.

Step 2

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.

Step 3

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.