Homework Help

Equation of the line.What is the equation of the line joining the midpoints of the...

user profile pic

potziunea | Student, Grade 10 | Honors

Posted May 18, 2011 at 7:55 AM via web

dislike 0 like
Equation of the line.

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)?

Tagged with discussion, math

1 Answer | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted May 18, 2011 at 10:30 AM (Answer #2)

dislike 0 like

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

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes