The point that bisects the line segment AB is (-1, 1)
Explanation:The point that will bisect the line segment AB will be the midpoint of AB
The midpoint(a, b) of the points (x₁, y₁) and (x₂, y₂) is given by the formulae:
[tex]\begin{gathered} a=\frac{x_1+x_2}{2} \\ b=\frac{y_1+y_2}{2} \end{gathered}[/tex]For the points A(-5, -2) and B(3, 4)
x₁ = -5, y₁ = -2, x₂ = 3, y₂ = 4
Substitute x₁ = -5, y₁ = -2, x₂ = 3, y₂ = 4 into the midpoint formulae:
[tex]\begin{gathered} a=\frac{x_1+x_2}{2} \\ a=\frac{-5+3}{2} \\ a=-\frac{2}{2} \\ a=-1 \end{gathered}[/tex][tex]\begin{gathered} b=\frac{y_1+y_2}{2} \\ b=\frac{-2+4}{2} \\ b=\frac{2}{2} \\ b=1 \end{gathered}[/tex]The midpoint of the line segment AB = (-1, 1)
Therefore, the point that bisects the line segment AB is (-1, 1)