Question

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


(StartFraction 3 Over 3 + 5 EndFraction) (2 minus (negative 14)) + (negative 14)

(StartFraction 3 Over 3 + 5 EndFraction) (negative 14 minus 2) + 2

(StartFraction 3 Over 3 + 5 EndFraction) (2 minus 14) + 14

StartFraction 3 Over 3 + 5 EndFraction (negative 14 minus 2) minus 2

Answer 1

A

Step-by-step explanation:

I just took the test

Answer 2

Option A:
`(3)/(3+5) (2-(-14))+(-14)` is the expression that correctly uses the formula
`(m)/(m+n) (x_2-x_1)+x_1`

Step-by-step explanation:

It is given that, the number 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.

Thus, we have,

`x_1=-14` ,
`x_2=2` ,
`m=3` and
`n=5`

The location of point R can be determined using the formula,

`(m)/(m+n) (x_2-x_1)+x_1`

Substituting the values, we get,

`(3)/(3+5) (2-(-14))+(-14)`

Hence, substituting the values
`x_1=-14` ,
`x_2=2` ,
`m=3` and
`n=5` in the formula
`(m)/(m+n) (x_2-x_1)+x_1`, we get,
`(3)/(3+5) (2-(-14))+(-14)`

Thus, the expression that correctly uses the formula is
`(3)/(3+5) (2-(-14))+(-14)`

Therefore, Option A is the correct answer.