Question

consider the line segment lp with endpoints at l(-3, -5) and p(9, 7) and midpoint m. what is the x - coordinate of n, the midpoint of line segment mp? enter the answer in the space provided. fractions should be entered in lowest terms using a forward slash (/) and converted to improper fractions when applicable. use only numbers, a negative sign (-), a decimal point (.), and/or a forward slash (/) to enter the answer.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For the $x$ - coordinate of the mid - point of two points $L(-3,-5)$ and $P(9,7)$, if the mid - point of $LP$ is $M$, the $x$ - coordinate of $M$ is $x_M=\frac{-3 + 9}{2}$.
$x_M=\frac{-3 + 9}{2}=\frac{6}{2}=3$.
Now, we want to find the $x$ - coordinate of the mid - point $N$ of $MP$. Let the coordinates of $M$ be $(3,y_M)$ (we don't need the $y$ - coordinate for this problem) and the coordinates of $P$ be $(9,7)$. Using the mid - point formula for the $x$ - coordinate again, if the mid - point of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is $(x_m,y_m)$, then $x_m=\frac{x_1 + x_2}{2}$. Here, $x_1 = 3$ and $x_2=9$.

Step2: Calculate the $x$ - coordinate of $N$

$x_N=\frac{3 + 9}{2}$.
$x_N=\frac{12}{2}=6$.

Answer:

$6$