How do I find the coordinates of the midpoint of a line segment with endpoints at (6, 4) and (2, 8)?

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To find the coordinates of the midpoint of a line segment defined by two endpoints, you can use the midpoint formula. The midpoint formula is given by:

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

Where:

  • (x1, y1) are the coordinates of the first endpoint
  • (x2, y2) are the coordinates of the second endpoint

In your case, the endpoints are:

  • First endpoint: (6, 4) where x1 = 6 and y1 = 4
  • Second endpoint: (2, 8) where x2 = 2 and y2 = 8

Now, let’s plug in these values into the midpoint formula:

(xm, ym) = \left( \frac{6 + 2}{2}, \frac{4 + 8}{2} \right)

Calculating the x-coordinate:

xm = \frac{6 + 2}{2} = \frac{8}{2} = 4

Calculating the y-coordinate:

ym = \frac{4 + 8}{2} = \frac{12}{2} = 6

So, the coordinates of the midpoint are:

(xm, ym) = (4, 6)

This means that the midpoint of the segment whose endpoints are (6, 4) and (2, 8) is the point (4, 6).

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