Question

What is the midpoint of line segment AB when A(-2,10) and B(6,-4)

Answer 1

Answer:

(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:

`\begin{gathered} a\text{ = }(x_1+x_2)/(2) \\ b\text{ = }(y_1+y_2)/(2) \end{gathered}`

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

`\begin{gathered} a\text{ = }(-2+6)/(2) \\ a\text{ = }(4)/(2) \\ a\text{ = 2} \\ b\text{ = }(10+(-4))/(2) \\ b\text{ = }(10-4)/(2) \\ b\text{ = }(6)/(2) \\ b\text{ = 3} \end{gathered}`

The midpoint of the line segment AB is therefore (2, 3)