Question

5. Find the ratio in which the line segment joining A(1,-5) and B(-4 5) is divided by the x axis .Also find the cordinates of the point of division ​

Answer 1

Answer:

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n is

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Now we have to find ratio

Let ratio be k:1

Hence

m

1

=k,m

2

=1

x

1

=1,y

1

=−5

x

2

=−4,y

2

=5

Also

x=x,y=0

Using section formula

y=

m

1

+m

2

m

1

y

2

+m

2

y

1

0=

k+1

k×5+1×(−5)

⇒0=

k+1

5k−5

⇒5k−5=0

⇒5k=5

∴k=1

Now, for x

x=

m

1

+m

2

m

1

x

2

+m

2

x

2

=

k+1

k×(−4)+1×1

=

1+1

1×(−4)+1

=

2

−4+1

=

2

−3

Hence the coordinate of point is P(x,0)=P(

2

−3

,0)