Question

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

Answer 1

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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