(2, 3)
Explanations:The coordinates of the midpoint (a, b) of the line with the endpoints (x₁, y₁ ) and (x₂, y₂) is given by the formulae:
[tex]\begin{gathered} a\text{ = }\frac{x_1+x_2}{2} \\ b\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]The line segment AB has endpoints A(-2,10) and B(6,-4)
Therefore:
x₁ = -2, y₁ = 10, x₂ = 6, y₂ = -4
Substitute these values into the formulae for the coordinates of the midpoints
[tex]\begin{gathered} a\text{ = }\frac{-2+6}{2} \\ a\text{ = }\frac{4}{2} \\ a\text{ = 2} \\ b\text{ = }\frac{10+(-4)}{2} \\ b\text{ = }\frac{10-4}{2} \\ b\text{ = }\frac{6}{2} \\ b\text{ = 3} \end{gathered}[/tex]The midpoint of the line segment AB is therefore (2, 3)
