Question

In what ratio the line joining the points (2,1) and (4,2) divides the line segment joining the points (2,3) and (4,-5)?  ​

Answer 1

Step-by-step explanation:

Let P(2,3),Q(4,1),R(1,2),S(4,3) be the points

Equation of PQ:

x−4

y−1

=

−2

2

⇒x+y=5 ___ (1)

Equation of RS:

x−4

y−3

=

3

1

⇒3y−x=(3)−(2)

Adding (1), (2), 4y=10⇒y=5/2,x=5/2

∴x(

2

5

,

2

5

) is the point of intersection

Let x divide RS in m:1 ratio, then

(

m+1

3m+2(1)

)=

2

5

[∵

m+n

my

2

+ny

1

=y]

6m+4=5m+5

m=1

∴ It divides RS in 1:1 ratio