On a number line, the directed line segment from Q to S has endpoints Q at −14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula open paren the fraction with numerator m and denominator m plus n close paren times open paren x sub 2 minus x sub 1 close paren plus x sub 1 to find the location of point cap r ?
Answer
A
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren 2 minus 14 close paren plus 14
B
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren 2 minus negative 14 close paren plus negative 14
C
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren negative 14 minus 2 close paren minus 2
D
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren negative 14 minus 2 close paren plus 2
Explanation
In the formula, x₁ is the starting point Q, so x₁ = −14, and x₂ is the endpoint S, so x₂ = 2. The 3:5 partition gives m = 3 and n = 5. Substituting gives (3/(3 + 5)) × (2 − (−14)) + (−14), which is choice B.
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