`Delta`PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map `Delta`PQR to `Delta`ABC, whose vertices are A(2, 4), B(5.5, 18), and C(12.5, 4). What is the scale factor of the dilation in the similarity transformation?
A.
2

B.
2.5

C.
4

D.
3.5

Notice that points P(2,4) and A(2,4) have the same coordinates, so we need to calculate the distances PQ and PR and compare them respectively to AB and AC, so:

[tex]PQ=\sqrt{(2-3)^{2}+(4-8)^{2} }[/tex]

[tex]PQ=\sqrt{17}[/tex]

and

[tex]PR=\sqrt{(2-5)^{2}+(4-4)^{2} }[/tex]

[tex]PR=3[/tex]

Now,

[tex]AB=\sqrt{(2-5.5)^{2}+(4-18)^{2} }[/tex]

[tex]AB=3.5*\sqrt{17}[/tex]

and

[tex]AC=\sqrt{(2-12.5)^{2}+(4-4)^{2} }[/tex]

[tex]AC=10.5[/tex]

Now let's find the ratios:

[tex]\frac{AB}{PQ} =\frac{3.5*\sqrt{17} }{\sqrt{17} } =3.5[/tex]

[tex]\frac{AC}{PR} =\frac{10.5}{3} =3.5[/tex]

In conclusion, the scale factor of the dilation is 3.5, so the answer is D.

`Delta`PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map `Delta`PQR to `Delta`ABC, whose vertices are A(2, 4), B(5.5, 18), and C(12.5, 4). What is the scale factor of the dilation in the similarity transformation? A. 2 B. 2.5 C. 4 D. 3.5

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`Delta`PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map `Delta`PQR to `Delta`ABC, whose vertices are A(2, 4), B(5.5, 18), and C(12.5, 4). What is the scale factor of the dilation in the similarity transformation?
A.
2

B.
2.5

C.
4

D.
3.5