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.

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