A line segment is bisected by a line with the equation # - 3 y + 5 x = 2 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?

1 Answer
Aditya Banerjee.
Nov 4, 2016

Long explanation !!

Explanation:

Slope #m_1# (say) of the line #-3y+5x=2# is :
#-3y=-5x+2# ...............(i)
#:.y=5/3x-2/3#
#:.m_1=5/3.#

Let slope of the line whose one end is #(7,9)# be #m_2# (say).
#:.m_1xxm_2=-1.# [The two lines are perpendicular to each other].

#:.5/3xxm_2=-1#
#:.m_2=-3/5.#

#:.# The equation of the line whose one end is #(7,9)# is :
#(y-y_1)=m(x-x_1)#
#:.# #:.(y-9)=-3/5(x-7)#
#:.3x+5y=66.# is the equation. ..............(ii)

Now, solving equations (i) & (ii), we get the value #(x,y)# which represents the midpoint of the line whose one end is #(7,9)#.

Now to find out the coordinates say, #(a,b)# of the other end, use Distance-Section formula.

#:.d=sqrt[(y_2-y_1)^2+(x_2-x_1)^2#.

#:.sqrt[(x-a)^2+(y-b)^2]=sqrt[(x-7)^2+(y-9)^2.#

Here, #(x,y)# is midpoint & #(a,b)# is the coordinate of the other required end.

Now, I leave it to you. Just put the values and solve.
Best of Luck.

Related questions
See all questions in Perpendicular Bisectors
Impact of this question
1485 views around the world
You can reuse this answer
Creative Commons License