# 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)?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to first find the midpoint of the lines segments joining the two pairs of points.

The midpoint of the line segment joining (6,2) and (8,4) is [ (6+8)/2, (2+4)/2] or ( 7, 3). The midpoint of the line segment joining (2,8) and (4,6) is [ (2+4)/2, (8+6)/2] or ( 3, 7).

Now for two points (x1, y1) and (x2, y2) the equation of the line joining them is y-y1 = [(y2-y1)/(x2 – x1)]*(x-x1)

The equation for the line between (3, 7) and (7, 3) is y – 7 = [(3-7)/ (7-3)]*(x-3)

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

=> y - 7 = 3 - x

=> x + y - 10 = 0

The required equation of the line is x + y - 10 =0

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The  mid points of (x1 , y1 ) and (x2, y2) is given by:

M(x , y) = (( x1+x2)/2 , (y1+y2)/2)).

Therefore the coordinates of mid point of (6,2) and (8,4)  are ((6+8)/2 , (2+4)/2) = (7, 3).

The coordinates mid point of (2,8) and (4,6) are given by: ((2+4)/2 , (8+6)/2)) = (3,7).

The  line joining (7,3) and (3,7) is to be found. We know that the line joining  the points (a1 , b1) and (a2, b2) is given by:

y- b1 = {(b2-b1)/(a2-a1)}(x-b1).

Therefore the line joing  (7,3) and (3,7)  is given by:

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

y-3 = -1(x-7)

x+y -3-7 = 0

x+y -10 = 0 is the required equation of the line .

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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