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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]



Answer :

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

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

Here, [tex]\(G(10, 1)\)[/tex] gives us [tex]\( x_1 = 10 \)[/tex] and [tex]\( y_1 = 1 \)[/tex], and [tex]\( H(3, 5) \)[/tex] gives us [tex]\( x_2 = 3 \)[/tex] and [tex]\( y_2 = 5 \)[/tex].

Plugging these values into the midpoint formula, we get:

[tex]\[ \text{Midpoint} = \left( \frac{10 + 3}{2}, \frac{1 + 5}{2} \right) \][/tex]

Now, let's calculate each component individually:

1. For the x-coordinate:
[tex]\[ \frac{10 + 3}{2} = \frac{13}{2} = 6.5 \][/tex]

2. For the y-coordinate:
[tex]\[ \frac{1 + 5}{2} = \frac{6}{2} = 3.0 \][/tex]

Thus, the coordinates of the midpoint of [tex]\( \overline{GH} \)[/tex] are:
[tex]\[ \left( 6.5, 3.0 \right) \][/tex]

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

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