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

1 Answer
sankarankalyanam
Oct 25, 2017

Coordinates of other endpoint (-13/5, -61/5)

Explanation:

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

Equation of line segment is
y - 7 = 2(x - 8)
2x - y = 9, Eqn (2)

Solving Eqns (1) & (2),
Midpoint coordinates x = 16/5, y = -13/5

Other end point coordinates (x_1, y_1)
(x_1+8)/2 = 16/5
#x_1 = -(8/5)

(y_1 +7)/2 = -13/5
y-1 = -(26/5) - 7 = -61/5

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