the point P(3,-2), divides the segment joining the points (x,0) and (0,y) in the ratio 1:3. Find x and y
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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
)
Given the points A(−4,3) and B(2,−4)
let P(a,−2) divides the join of A(−4,3)≡(x
1
,y
1
)and B(2,8)≡(x
2
,y
2
) in the ratio K:1
⇒P(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)=P(
K+1
2K−4
,
K+1
−4K+3
)
∴
K+1
2K−4
=a,
K+1
−4K+3
=−2
−4K+3=−2(K+1)
⇒−4K+3=−2K−2
⇒−2K=−5
∴K=
2
5
Hence the ration of divison is 5:2
∴a=
K+1
2K−4
=
2
5
+1
2×
2
5
−4
=
5+2
(5−4)2
=
7
2
∴ value of a=
7
2
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