Question

`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

Answer 1

The answer to this is D, 3.5

Answer 2

D. 3.5

Explanation:

In order to find the answer we can use the distance equation as follows:

`D=\sqrt{(x1-x2)^(2)+(y1-y2)^(2) }`

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:

`PQ=\sqrt{(2-3)^(2)+(4-8)^(2) }`

`PQ=√(17)`

and

`PR=\sqrt{(2-5)^(2)+(4-4)^(2) }`

`PR=3`

Now,

`AB=\sqrt{(2-5.5)^(2)+(4-18)^(2) }`

`AB=3.5*√(17)`

and

`AC=\sqrt{(2-12.5)^(2)+(4-4)^(2) }`

`AC=10.5`

Now let's find the ratios:

`(AB)/(PQ) =(3.5*√(17) )/(√(17) ) =3.5`

`(AC)/(PR) =(10.5)/(3) =3.5`

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