Question

use the given endpoint r and mid - point m of line segment rs to find the coordinates of the x - value of the endpoint s. r(15,0) m(7,25) s(x,50)

Explanation:

Step1: Recall mid - point formula for x - coordinate

The mid - point formula for the x - coordinate of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ and mid - point $(x_m,y_m)$ is $x_m=\frac{x_1 + x_2}{2}$. Here, let $R(15,0)$ be $(x_1,y_1)$, $S(x,50)$ be $(x_2,y_2)$ and $M(7,25)$ be $(x_m,y_m)$. We only care about the x - coordinates, so $x_m=\frac{x_1 + x_2}{2}$ becomes $7=\frac{15 + x}{2}$.

Step2: Solve the equation for x

Multiply both sides of the equation $7=\frac{15 + x}{2}$ by 2: $7\times2=15 + x$, which simplifies to $14 = 15+x$. Then subtract 15 from both sides: $x=14 - 15=-1$.

Answer:

-1