A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that the P lies on the line x + y = 0, then find the value of k:1 and the point P
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Answer
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
The ratio is k:1 and, x
1
=3,x
2
=−4,y
1
=−5,y
2
=8
Coordinates of point P
=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
=(
k+1
k(−4)+1(3)
,
k+1
k(8)+1(−5)
)----------[m=k,n=1]
=(
k+1
−4k+3
,
k+1
8k−5
)
Now,
k+1
−4k+3
+
k+1
8k−5
=0
⇒4k−2=0
⇒k=
4
2
=
2
1
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