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3 years ago

Points A, B, C, and D lie on a line in that order. If AD/AC = 2/1 and AD/AB = 3/1, what is the value of AC/BD?

Mathematics

1 answer:

VashaNatasha [74]3 years ago

7 0

9514 1404 393

Answer:

3/4

Step-by-step explanation:

It might be easier to start by expressing the ratios with AD as the denominator.

AD/AC = 2/1 ⇒ AC/AD = 1/2

AD/AB = 3/1 ⇒ AB/AD = 1/3

From the latter, we have ...

(AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD

Then the desired ratio is ...

AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)

AC/BD = 3/4

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