on a number line, the directed line segment from q to s has endpoints q at -14 and s at 2. point r…

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 $left(\frac{m}{m + n}\right)(x_2 - x_1)+x_1$ to find the location of point r? $left(\frac{3}{3 + 5}\right)(2-(-14))+(-14)$ $left(\frac{3}{3 + 5}\right)(-14 - 2)+2$ $left(\frac{3}{3 + 5}\right)(2 - 14)+14$ $left(\frac{3}{3 + 5}\right)(-14 - 2)-2$

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 $left(\frac{m}{m + n}\right)(x_2 - x_1)+x_1$ to find the location of point r? $left(\frac{3}{3 + 5}\right)(2-(-14))+(-14)$ $left(\frac{3}{3 + 5}\right)(-14 - 2)+2$ $left(\frac{3}{3 + 5}\right)(2 - 14)+14$ $left(\frac{3}{3 + 5}\right)(-14 - 2)-2$

Answer

Explanation:

Step1: Identify values of m, n, x1, x2

Given ratio is 3:5, so $m = 3$, $n=5$. $x_1$ is the x - coordinate of Q which is - 14, $x_2$ is the x - coordinate of S which is 2.

Step2: Substitute values into formula

Substitute $m = 3$, $n = 5$, $x_1=-14$, $x_2 = 2$ into the formula $\left(\frac{m}{m + n}\right)(x_2 - x_1)+x_1$. We get $\left(\frac{3}{3 + 5}\right)(2-(-14))+(-14)$.

Answer:

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