Answer: The required co-ordinates of the midpoint are (-3, -1).
Step-by-step explanation: Given that the endpoints of the line segment LM are L(-1,1) and M(-5,-3).
We are to find the co-ordinates of the midpoint of segment LM.
We know that,
the co-ordinates of the midpoint of a line segment with and points (a, b) and (c, d) are given by
[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, the co-ordinates of the midpoint of segment LM are
[tex]\left(\dfrac{-1+(-5)}{2},\dfrac{1+(-3)}{2}\right)\\\\\\=\left(\dfrac{-1-5}{2},\dfrac{1-3}{2}\right)\\\\\\=\left(\dfrac{-6}{2},\dfrac{-2}{2}\right)\\\\\\=(-3,-1).[/tex]
Thus, the required co-ordinates of the midpoint are (-3, -1).
