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{ = }((x_1+x_2)/(2),(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{ = (}(1+6)/(2),(-1+(-8))/(2)) \\ =\text{ (}(7)/(2),(-9)/(2)) \end{gathered}`

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