How do you find the midpoint of the line segment with endpoints (7, 5) and (7, 11)?

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Finding the Midpoint of a Line Segment

The midpoint of a line segment is the point that is exactly halfway between the two endpoints. To find the midpoint between the endpoints (7, 5) and (7, 11), we use the midpoint formula.

Midpoint Formula

The formula to calculate the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is:

M = \\left(\\frac{x1 + x2}{2}, \\frac{y1 + y2}{2}\\right)

Applying the Formula

For our specific endpoints:

  • (x1, y1) = (7, 5)
  • (x2, y2) = (7, 11)

We can plug these values into the formula:

M = \\left(\\frac{7 + 7}{2}, \\frac{5 + 11}{2}\\right)

Now, we calculate each component:

  1. For the x-coordinate: \\frac{7 + 7}{2} = \\frac{14}{2} = 7
  2. For the y-coordinate: \\frac{5 + 11}{2} = \\frac{16}{2} = 8

Final Midpoint

Thus, the midpoint M of the line segment with endpoints (7, 5) and (7, 11) is:

M = (7, 8)

This means the point (7, 8) lies exactly halfway between the given endpoints. You can visualize this point as being directly in the middle of the vertical segment that connects (7, 5) and (7, 11) on a Cartesian plane.

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