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3. The formula for the midpoint between two points [tex]\left(x_1, y_1\right),\left(x_2, y_2\right)[/tex] is [tex]\left(\frac{\left(x_1+x_2\right)}{2}, \frac{\left(y_1+y_2\right)}{2}\right)[/tex].

Segment [tex]\overline{GH}[/tex] has endpoints [tex]G(-3,7)[/tex] and [tex]H(-3,-7)[/tex]. What are the coordinates of the midpoint of [tex]\overline{GH}[/tex]?

A. [tex]\left(-2 \frac{1}{2}, 0\right)[/tex]
B. [tex](-3,-7)[/tex]
C. [tex](3,-3)[/tex]
D. [tex](-3,0)[/tex]

Sagot :

GinnyAnsweridn
To find the midpoint of a line segment with endpoints [tex]\( G(-3,7) \)[/tex] and [tex]\( H(-3,-7) \)[/tex], we use the midpoint formula:

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

where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the endpoints. In this case, [tex]\( G \)[/tex] has coordinates [tex]\((-3, 7)\)[/tex] and [tex]\( H \)[/tex] has coordinates [tex]\((-3, -7)\)[/tex].

1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{-3 + (-3)}{2} = \frac{-3 - 3}{2} = \frac{-6}{2} = -3 \][/tex]

2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{7 + (-7)}{2} = \frac{7 - 7}{2} = \frac{0}{2} = 0 \][/tex]

Therefore, the coordinates of the midpoint of [tex]\(\overline{GH}\)[/tex] are:

[tex]\[ (-3, 0) \][/tex]

Among the provided options, the correct coordinates of the midpoint of [tex]\(\overline{GH}\)[/tex] are:

[tex]\[ (-3, 0) \][/tex]
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