A line segment is bisected by a line with the equation 3 y - 7 x = 2 . If one end of the line segment is at ( 8 , 1 ), where is the other end?

1 Answer
sankarankalyanam
Oct 14, 2017

Coordinates of other end points (-6.6,3.6)

Explanation:

Assumption : Bisecting line is a perpendicular bisector

Standard form of equation y=max+c
Slope of perpendicular bisector m is given by
3y-7x=2
y=(7/3)x+(2/3)
m=7/3
Slope of line segment is
y-1=-(1/m)(x-8)
y-1=-(3/7)(x-8)
7y-7=3x-24

7y-3x=-14color(white)((aaaa) Eqn (1)
3y-7x=2color(white)((aaaa) Eqn (2)

Solving Eqns (1) & (2),
21y-9x=42
21y-49x=14
Subtracting and eliminating y term,
40x=28
x=7/10
Substituting value of x in Eqn (1),
7y-(21/10)=14
y=(161/10)/7=23/10
Mid point #(7/10,23/10)

Let (x1,y1) the other end point.
(8+x1)/2=7/10
x1=-6.6
(1+y1)/2=23/10
y1=3.6

Coordinates of other endpoint (-6.6,3.6)

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