The Mid - point of the line segment is at coordinates - M(- 7.5, 0.5)
We have two coordinate points - A(- 10, 2) and B(- 5, -1)
We have to find the midpoint of this line AB.
It states that a line with endpoint coordinates as - [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] has its mid - point at the coordinates -
[tex](x_{M} ,y_{M} ) =( \frac{x_{1} +x_{2} }{2} , \frac{(y_{1} +y_{2} )}{2} )[/tex]
According to question, we have -
First coordinate Point - [tex](x_{1} ,y_{1} )[/tex] = (- 10, 2)
Second coordinate Point - [tex](x_{2} ,y_{2} )[/tex] = (- 5, - 1)
Using the Mid - Point formula, we get -
[tex](x_{M} ,y_{M} ) =( \frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex] =
[tex]x_{M} = \frac{-10-5}{2} = \frac{-15}{2} = - 7.5\\\\y_{M} = \frac{2 - 1}{2} = \frac{1}{2} = 0.5[/tex]
Hence, the Mid - point of the line segment is at coordinates -
M(- 7.5, 0.5)
To solve more questions on Mid - points, visit the link below -
https://brainly.com/question/25377004
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