What is the equation of the line joining the midpoints of the lines joining (6,2) and (8,4) and (2, 8) and (4, 6)?

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The equation of a line that passes through 2 points, whose coordinates are known is:

(xM-xN)/(x-xM) = (yM-yN)/(y-yN)

We'll calculate xM and yM:

xM = (6+8)/2

xM = 7

yM = (2+4)/2

yM = 3

The coordinates of the midpoint of the line that passes through (6,2) and (8,4) is M(7,3).

xN = (2+4)/2

xN = 3

yN = 7

The coordinates of the midpoint of the line that passes through (2, 8) and (4, 6) is N(3,7).

The line that passes through the points M and N is:

(3-7)/(x-7) = (7-3)/(y-3)

-4/(x-7) = 4/(y-3)

We'll divide by 4 both sides:

-1/(x-7) = 1/(y-3)

-y+3 = x-7

The equation of the line that passes through the midpoints M and N is:

x + y - 10 = 0

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