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The endpoints of [tex]\overline{GH}[/tex] are [tex]G(10,1)[/tex] and [tex]H(3,5)[/tex]. What is the midpoint of [tex]\overline{GH}[/tex]?

A. [tex](-4,9)[/tex]
B. [tex]\left(\frac{7}{2}, 2\right)[/tex]
C. [tex]\left(\frac{13}{2}, 3\right)[/tex]
D. [tex](13,6)[/tex]


Sagot :

To find the midpoint of the line segment with endpoints [tex]\( G(10, 1) \)[/tex] and [tex]\( H(3, 5) \)[/tex], we use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:

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

Here, we have the coordinates [tex]\( G(10, 1) \)[/tex] and [tex]\( H(3, 5) \)[/tex].

First, calculate the x-coordinate of the midpoint:
[tex]\[ x_{\text{midpoint}} = \frac{10 + 3}{2} = \frac{13}{2} \][/tex]

Next, calculate the y-coordinate of the midpoint:
[tex]\[ y_{\text{midpoint}} = \frac{1 + 5}{2} = 3 \][/tex]

Therefore, the midpoint of [tex]\(\overline{GH}\)[/tex] is:
[tex]\[ \left( \frac{13}{2}, 3 \right) \][/tex]

So, the correct answer is:
[tex]\[ \boxed{\left( \frac{13}{2}, 3 \right)} \][/tex]