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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 :

GinnyAnswer
To determine the midpoint of the line segment \(\overline{GH}\) with endpoints \(G(10,1)\) and \(H(3,5)\), we use the midpoint formula. The midpoint formula is:

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

Here, \((x_1, y_1) = (10, 1)\) and \((x_2, y_2) = (3, 5)\).

1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{10 + 3}{2} = \frac{13}{2} \][/tex]

2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3 \][/tex]

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

So, the correct answer is:

C. [tex]\(\left( \frac{13}{2}, 3 \right)\)[/tex]
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