Question

Find the ratio in which the line segment joining the points (1 - 3) and (4 ,5) is divided by x-axis.​

Answer 1

Step-by-step explanation:

Let the line segment joining the point (1,-3) and (4,5) is divided by x axis is k:1 and the point of intersection be (x,0).

Section formula,

P(x,y)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})P(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Using section formula, we get

\frac{my_2+ny_1}{m+n}=0

m+n

my

2

+ny

1

=0

\frac{k(5)+1(-3)}{k+1}=0

k+1

k(5)+1(−3)

=0

5k-3=05k−3=0

k=\frac{3}{5}k=

5

3

The x-axis divides the line segment joining the point (1,-3) and (4,5) is 3:5.

Using section formula, we get

\frac{mx_2+nx_1}{m+n}=\frac{3(4)+5(1)}{3+5}=\frac{17}{8}

m+n

mx

2

+nx

1

=

3+5

3(4)+5(1)

=

8

17

Therefore the point of intersection is (\frac{17}{8},0)(

8

17

,0) .