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
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#