A line segment is bisected by line with the equation 6 y - 2 x = 1 . If one end of the line segment is at (4 ,1 ), where is the other end?

1 Answer
sankarankalyanam
Oct 25, 2017

Coordinates of other endpoint (-107/10, -29/10)

Explanation:

Assumption : Its a perpendicular bisector.
Slope of line = m_1
6y = 2x + 1 , Eqn (1)
y = (1/3)x + (1/6)
m_1 = 1/3
Slope of line segment (perpendicular) m_2 = -1/m_1 = -3

Equation of line segment is
y - 1 = -3(x - 4)
3x + y = -11, Eqn (2)

Solving Eqns (1) & (2),
Midpoint coordinates x = -67/20, y = -19/20

Other end point coordinates (x_1, y_1)
(x_1+4)/2 = -67/20
x_1 = -107/10

(y_1 +1)/2 = -19/20
y-1 = -29/10

Related questions
See all questions in Perpendicular Bisectors
Impact of this question
2182 views around the world
You can reuse this answer
Creative Commons License