Question

A line segment has endpoints P (3, 6) and Q (12, 18) and is dilated so that its new endpoints are P’ (2, 4) and Q’ (8, 12). What is the scale factor? If the length of PQ is 15, what is the length of P’Q’?

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Answer 1

It should be 14, because 8 - 2 = 6 and 12 - 4 = 8

Answer 2

Scale Factor ≈ 0.67

P'Q' Length = 10

Explanation:

To find the scale factor, a relationship must be found between the original points, and the dilated points. To do this, simply divide the new points by the old points.

P to P' :
`(2)/(3)=0.6667` AND
`(4)/(6)=0.6667`

Q to Q' :
`(8)/(12)=0.6667` AND
`(12)/(18)=0.6667`

Therefore, the scale factor is 0.6667 ≈ 0.67

The length of P'Q' can be calculated with the distance formula:

`d^(2)=(y_(1)-y_(2) )^(2) +(x_(1)-x_(2) )^(2) \\d^(2) =(4-12)^(2) + (2-8)^(2) \\d^(2) =(-8)^(2) +(-6)^(2) \\d^(2) =64+36\\d=√(100) =10`

Alternatively, you could multiply the length of PQ with the scale factor to find P'Q':

15*0.6667=10