Question

Write down the equation of the line whose slope is -1 and which passes through P, where P divides the line segment joining A (-1,2) and B (3,6) in the ratio 1:3​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

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(−4)+3(6)/2+3

= 10/5 =2

∴P≡(0,2)

Now, the equation of the line having slope  3/2 and passing through P(0,2) is

y−2=

3/2 (x−0)

i.e. 2y−4=3x

3x−2y+4=0

Thus, the equation of the required line is

3x−2y+4=0.