Question

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Answer 1

Answer:

Suppose the point P(−3,p) divides the line segment joining points A(−5,−4)≡(x

2

,y

2

) and B(−2,3)≡(x

1

,y

1

) in the ratio k:1.

Section formula: [x=(

m+n

mx

1

+nx

2

)] and [y=(

m+n

my

1

+ny

2

)]

Then, the coordinates of P are(

k+1

−2k−5

k+1

3k−4

)

But, the coordinates of P are given as (−3,p).

∴

k+1

−2k−5

=−3and

k+1

3k−4

=p

⇒−2k−5=−3k−3and

k+1

3k−4

=p

⇒k=2andp=

k+1

3k−4

⇒k=2andp=

3

2

Hence, the ratio is 2:1 and p=

3

2

Answer 2

Answer:

Explanation:

Suppose the point P(−3,p) divides the line segment joining points A(−5,−4)≡(x 2,y 2) and B(−2,3)≡(x1,y1) in the ratio k:1. Section formula: [x=( m+nmx 1 +nx 2 )] and [y=( m+n my 1 +ny 2 )] Then, the coordinates of P are( k+1 −2k−

k+13k−4) But, the coordinates of P are given as (−3,p). ∴ k+1 −2k−5 =−3and +1 3k−4 =p ⇒−2k−5=−3k−3and k+1 3k−4 =p ⇒k=2andp= k+1 3k−4 ⇒k=2andp=3 2 Hence, the ratio is 2:1 and p= 3 2

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