The midpoint of a line segment given in the graph will be [tex](\frac{7}{2}, 4 )[/tex], i.e. option B.
What is midpoint of a line segment?
A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments. The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
i.e.
Mid-point [tex]=(\frac{x_1 + x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
We have,
Let,
Point A = (2, -1)
i.e. x₁ = 2, y₁ = -1
And,
Point B = (5, 9)
i.e. x₂ =5, y₂ = 9
So,
Using the formula mentioned above,
Mid-point [tex]=(\frac{x_1 + x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
i.e.
Mid-point [tex]=(\frac{2+ 5}{2}, \frac{-1+9}{2} )[/tex]
So,
On solving we get,
Mid-point [tex]=(\frac{7}{2}, 4 )[/tex]
So, the mid point of the given segment is [tex](\frac{7}{2}, 4 )[/tex].
Hence, we can say that the midpoint of a line segment given in the graph will be [tex](\frac{7}{2}, 4 )[/tex], i.e. option B.
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