Question

What is the midpoint of the line segment graphed below?10(1,-1)1010(6,8)10

Answer 1

The points that make up the line segment are :

(1,-1) and (6, -8)

Solution

The mid-point of a line segment with the coordinates of the points as:

$\begin{gathered} \text{first point : (x}_1,y_1)\text{ } \\ \text{second point: (x}_2,y_2) \end{gathered}$

can be calculated using the formula:

$\begin{gathered} (x_m,y_m)\text{ = }(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{where x}_m,y_m\text{ are the coordinates of the mid-point} \end{gathered}$

By substituting the given points (1, -1) and (6, -8), we have:

$\begin{gathered} (x_m,y_m)\text{ = (}\frac{1+6}{2},\frac{-1+(-8)}{2}) \\ =\text{ (}\frac{7}{2},\frac{-9}{2}) \end{gathered}$

Answer: (7/2, -9/2)