Question

Problem 2: Find the midpoint of the line segment with the given endpoints 1. (-3,-5) (4,5) 2. (-3,8) (1,-9)

Answer 1

The given points are (-3,-5) and (4,5). To find the midpoint between these two, we use the following formula.

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Where,-

`\begin{gathered} x_1=-3,x_2=4 \\ y_1=-5,y_2=5 \end{gathered}`

Replacing these coordinates in the formula, we have

`\begin{gathered} M=((-3+4)/(2),(-5+5)/(2)) \\ M=((1)/(2),(0)/(2)) \\ M=((1)/(2),0) \end{gathered}`

Therefore, the midpoint is (1/2, 0).

Similarly, for the points (-3,8) and (1,-9), we use the same process as we did above.-

`\begin{gathered} M=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ M=((-3+1)/(2),(8-9)/(2)) \\ M=((-2)/(2),(-1)/(2)) \\ M=(-1,-(1)/(2)) \end{gathered}`

Therefore, the midpoint is (-1, -1/2).