# Find the equation of the line whose slope is 4/5 and which bisects te line joining the points P(1,2) and and Q(4,-3)

2
by anudeepd2

2014-10-23T10:21:56+05:30

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So the midpoint of P and Q is
x = (1+4)/2 = 5/2
y = (2 - 3)/2  = -1/2

so the mid point be Z(5/2,-1/2)

so the line is

(y+1/2) = 4/5(x - 5/2)

⇒(2y + 1)/2 = 4/5(2x - 5)/2

⇒10y + 5 = 8x - 20

⇒8x - 10y - 25 = 0 ANSWER

i know but some users are just
just
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don't understand
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2014-10-23T15:29:28+05:30
Given ,
slope of the equation = 4/5
and passing through the line of points p(1,2) and q(4,-3)
the line bisects it means passing through the mid point.
mid point of points p(1,2) and q(4,-3) is
[  (1+4)/2 , (2-3)/2 ]
=( 5/2 , -1/2 )

so the line equation is ( y-y1 ) = m ( x-x1 )
( y+1/2 ) = 4/5 ( x-5/2 )
(2y+1)/2  = 4/5 (2x-5)/2
(2y+1)/2 = (8x-20)/10
(2y+1)5 = 8x-20
10y+5 = 8x-20
8x-10y-25=0