A line segment is bisected by line with the equation 6 y - 7 x = 3 . If one end of the line segment is at (7 ,2 ), where is the other end?

1 Answer
sankarankalyanam
Oct 9, 2017

Other end point is (103/51,130/17)

Explanation:

Assumption : It’s a perpendicular bisector.
6y-7x=3 Eqn (1)
y=(7/6)x+cancel(3/6)(1/2)
It’s in the form y=mx+c where m is the slope.
:.m=7/6. Slope of perpendicular line is -(6/7)
Equation of line segment is
y-2=-(6/7)(x-7)
7y-14=-6x+42
7y+6x=56 Eqn (2)

Solving Eqns (1) & (2)
36y-42x=18
49y+42x=392 Adding,
85y=410
y=410/85=82/17
x=(56-7y)/6=(56-(6*82)/17))/6=(952-492)/102=460/102=230/51

Mid point =(230/51,82/17) One end point =(7,2) Other end point be (x1,y1)
(x1+7)/2=230/51
x1=(460/51)-7=(460-357)/51=103/51
(y1+2)/2=82/17
y1=(164/17)-2=(164-34)/17=130/17
Other end point is (103/51,130/17)

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