Question

Several transformations are used to create the pattern.

Part A

Describe the transformation of triangle GLM to triangle DGH.

Part B

Describe the transformation of triangle ALQ to triangle GLM.

Part C

Triangle DFN is a dilation of triangle GHM. Find the scale factor.

Answer 1

Step 1: Find the transformation of $△\mathrm{GLM}$ to $△\mathrm{DGH}$.

Given, figure

From the figure, we can see that the both $△\mathrm{GLM}$ and $△\mathrm{DGH}$ are of the same shape and same size but their position are different. So, the one of them would be translated to get the second one.

So, the transformation will be translated.

Step 2: Find the transformation of $△\mathrm{ALQ}$ to $△\mathrm{GLM}$.

From the figure we can see that the seize of the $△\mathrm{ALQ}$ is four times the size of $△\mathrm{GLM}$ and the shape of both triangles is the same. So, the one of them would be dilated with scale factor $4$ to get the second one.

So, the transformation is dilation.

Step 3: Find the scale factor for $△\mathrm{DFN}$ to $△\mathrm{GHM}$.

From the given figure, we can see that the size of $△\mathrm{DFN}$ is double the size of $△\mathrm{GHM}$. But, the shape of both is same, So, one of them would be dilated with scale factor $2$ to get the second one.

Hence, the transformation will be dilation.