Write down the equation of a line whose slope is 3/2 and which passes through point P, where
P divides the line segment AB joining A(-2,6) and B(3,-
4) in the ratio 2:3.
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Write down the equation of a line whose slope is
2
3
and which passes through point P, where P divides the line segment AB joining A(−2,6) and B(3,−4) in the ratio 2:3
October 15, 2019avatar
Saptarshi Rathod
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ANSWER
Here, A≡(−2,6)=(x
1
,y
1
)
B≡(3,−4)=(x
2
,y
2
)
P divides segAB internally in the ratio 2:3
∴m:n=2:3
Let P≡(x,y)
We have,
x=
m+n
mx
2
+nx
1
=
2+3
2(3)+3(−2)
=
5
0
=0
and y=
m+n
my
2
+ny
1
=
2+3
2(−4)+3(6)
=
5
10
=2
∴P≡(0,2)
Now, the equation of the line having slope
2
3
and passing through P(0,2) is
y−2=
2
3
(x−0)
i.e. 2y−4=3x
3x−2y+4=0
Thus, the equation of the required line is
- 3x−2y+4=0.
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