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What is the midpoint of the line segment with endpoints [tex]$(-5.5, -6.1)$[/tex] and [tex]$(-0.5, 9.1)$[/tex]?

A. [tex][tex]$(-6, 3)$[/tex][/tex]
B. [tex]$(-3, 3)$[/tex]
C. [tex]$(-3, 1.5)$[/tex]
D. [tex][tex]$(-6, 1.5)$[/tex][/tex]


Sagot :

To find the midpoint of a line segment with given endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula:

[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Let's apply this formula step-by-step to the endpoints [tex]\((-5.5, -6.1)\)[/tex] and [tex]\((-0.5, 9.1)\)[/tex]:

1. First, calculate the x-coordinate of the midpoint:
[tex]\[ \frac{-5.5 + (-0.5)}{2} = \frac{-5.5 - 0.5}{2} = \frac{-6}{2} = -3.0 \][/tex]

2. Next, calculate the y-coordinate of the midpoint:
[tex]\[ \frac{-6.1 + 9.1}{2} = \frac{3.0}{2} = 1.5 \][/tex]

Therefore, the coordinates of the midpoint are [tex]\((-3.0, 1.5)\)[/tex].

Comparing this result with the provided choices, the correct answer is:
C. [tex]\((-3,1.5)\)[/tex]
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