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Equation of the line.What is the equation of the line joining the midpoints of the...
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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
Posted by giorgiana1976 on May 18, 2011 at 10:30 AM (Answer #2)
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