Ray Martinez
04/30/2023 · Middle School
oint of the segment given its endpoints. 7.M(-5,9) and \( N(-2,7) \) 7)
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Tutor-Verified Answer
Step-by-step Solution
To find the midpoint of a line segment given its endpoints \( M(-5, 9) \) and \( N(-2, 7) \), you can use the midpoint formula:
\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Where \( (x_1, y_1) \) are the coordinates of point \( M \) and \( (x_2, y_2) \) are the coordinates of point \( N \).
Substituting the coordinates of points \( M \) and \( N \):
- \( x_1 = -5 \)
- \( y_1 = 9 \)
- \( x_2 = -2 \)
- \( y_2 = 7 \)
Now, plug these values into the formula:
\[
\text{Midpoint} = \left( \frac{-5 + (-2)}{2}, \frac{9 + 7}{2} \right)
\]
Calculating the x-coordinate:
\[
\frac{-5 - 2}{2} = \frac{-7}{2} = -3.5
\]
Calculating the y-coordinate:
\[
\frac{9 + 7}{2} = \frac{16}{2} = 8
\]
Thus, the midpoint of the segment \( MN \) is:
\[
\text{Midpoint} = \left( -3.5, 8 \right)
\]
Quick Answer
The midpoint of the segment \( MN \) is \( (-3.5, 8) \).
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