On a number line, the directed line segment from cap q to cap s has endpoints cap q at negative 8 and cap s at 12 Point cap r partitions the directed line segment from cap q to cap s in a ratio of 4 to 1 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 4 and denominator 4 plus 1 close paren times open paren 12 minus negative 8 close paren plus negative 8
B
open paren the fraction with numerator 4 and denominator 1 plus 4 close paren times open paren negative 8 minus 12 close paren plus 12
C
open paren the fraction with numerator 4 and denominator 4 plus 1 close paren times open paren negative 8 minus 12 close paren plus 12
D
open paren the fraction with numerator 1 and denominator 1 plus 4 close paren times open paren 12 minus negative 8 close paren plus negative 8
Explanation
In the formula, x₁ is the starting endpoint q = −8 and x₂ is the ending endpoint s = 12. The ratio 4 to 1 gives m = 4 and n = 1, so the expression is (4/(4 + 1)) × (12 − (−8)) + (−8). This matches choice A.
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