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

1 Answer
sankarankalyanam
Oct 20, 2017

Coordinates of other end = (67/29, 8/29) or (2.3103, 0.2759)

Explanation:

Assumption : Given line equation is a perpendicular bisector to the line segment

3x - 7y = 2 color (white)(aaa) Eqn (1)
y = (3/7)x - (2/7)
Slope of line m1 = 3/7.
Slope of perpendicular line segment = -1 / (m1 )= -1 / (3/7) = -7/3

y - 1 = -(7/3) (x - 2)
#7x + 3y = 17 color(white)(aaa) Eqn (2)

Solving Eqns (1) & (2),
x = 125/58, y = 37/58

(2+x_1) / 2 = 125/58
x_1 = (125 - 58)/ 29 =67/29
(1+y_1) / 2 = 37/58
y_1 = 8/29

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