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

Option A: $\frac{3}{3+5} (2-(-14))+(-14)$ is the expression that correctly uses the formula $\frac{m}{m+n} (x_2-x_1)+x_1$

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,

$\frac{m}{m+n} (x_2-x_1)+x_1$

Substituting the values, we get,

$\frac{3}{3+5} (2-(-14))+(-14)$

Hence, substituting the values $x_1=-14$ , $x_2=2$ , $m=3$ and $n=5$ in the formula $\frac{m}{m+n} (x_2-x_1)+x_1$, we get, $\frac{3}{3+5} (2-(-14))+(-14)$

Thus, the expression that correctly uses the formula is $\frac{3}{3+5} (2-(-14))+(-14)$

Therefore, Option A is the correct answer.

Answer 2

Answer:

A

Step-by-step explanation:

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