∆PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map ∆PQR to ∆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?

Question

12-07-2024
Mathematics

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∆PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map ∆PQR to ∆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?

Sagot :

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sqdancefan sqdancefan · Answer 1 · 2024-07-12T16:03:20-04:00

Answer:

3.5

Step-by-step explanation:

You want the scale factor in the dilation that maps P(2, 5), Q(3, 8), R(5, 4) to A(2, 4), B(5.5, 18), C(12.5, 4).

Scale factor

We can determine the scale factor by looking at the lengths of PQ and AB. The first step in determining the length will be to form the differences Q-P and B-A. Since there are no rotations involved, we only need to look at the differences of the x-coordinates.

Qx -Px = 3 -2 = 1

Bx -Ax = 5.5 -2 = 3.5

The scale factor of the dilation is ...

[tex]s=\dfrac{B_x-A_x}{Q_x-P_x}=\dfrac{3.5}{1}=3.5[/tex]

The scale factor of the dilation is 3.5.

∆PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map ∆PQR to ∆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?

Sagot :

Scale factor

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