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What is the midpoint of a line segment with the endpoints [tex]\((8, -3)\)[/tex] and [tex]\((-5, -9)\)[/tex]?

A. [tex]\((-7, 2.5)\)[/tex]

B. [tex]\((2.5, -7)\)[/tex]

C. [tex]\((-6, 1.5)\)[/tex]

D. [tex]\((1.5, -6)\)[/tex]

Sagot :

GinnyAnswer
To find the midpoint of a line segment defined by two endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula. The formula for the midpoint [tex]\((M_x, M_y)\)[/tex] of the line segment is:

[tex]\[ M_x = \frac{x_1 + x_2}{2} \][/tex]
[tex]\[ M_y = \frac{y_1 + y_2}{2} \][/tex]

Given the endpoints are [tex]\((8, -3)\)[/tex] and [tex]\((-5, -9)\)[/tex], we can substitute these values into the formula:

[tex]\[ M_x = \frac{8 + (-5)}{2} = \frac{8 - 5}{2} = \frac{3}{2} = 1.5 \][/tex]

[tex]\[ M_y = \frac{-3 + (-9)}{2} = \frac{-3 - 9}{2} = \frac{-12}{2} = -6 \][/tex]

Therefore, the coordinates of the midpoint are [tex]\((1.5, -6)\)[/tex].

The correct answer is:
D. [tex]\((1.5, -6)\)[/tex]
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