Answer and Step-by-step explanation:
1.
We are told to give the transformations needed to map the triangle ABC onto the triangle XYZ.
First off, we should move the triangle to the right. We need to have point B of triangle ABC to overlap point Y of triangle XYZ.
Once that is done, we need to do a dilation by scale 1.5. This would perfectly align triangle ABC onto triangle XYZ.
2.
To find the length of XZ, we need to find the dilation factor. Since we know that the triangles are similar, we can divide the bigger side by the little side (though only the sides that correspond).
We will divide side CB by ZY to get the dilation scale factor.
6 divided by 4 equals 1.5.
Now, to find the length, we will divide side CA by 1.5.
21 divided by 1.5 equals 14.
The length of ZY is 14.
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