Question

On a number line, the directed line segment from Q to S has endpoints Q at –8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio.

Which expression correctly uses the formula (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 to find the location of point R?

(StartFraction 1 Over 1 + 4 EndFraction) (12 minus (negative 8)) + (negative 8)
(StartFraction 4 Over 4 + 1 EndFraction) (12 minus (negative 8)) + (negative 8)
(StartFraction 4 Over 4 + 1 EndFraction) (negative 8 minus 12) + 12
(StartFraction 4 Over 1 + 4 EndFraction) (negative 8 minus 12) + 12

Answer 1

The second expression.

Reason: R is 4/5 of the way from Q(x1 = -8) to S(x2 = 12), so use (4/(4+1))(12 - (−8)) + (−8) = (4/5)(20) − 8 = 16 − 8 = 8.