Question

Find the ratio in line segment joining the points (6,4)and(1,-70 is divided by x axis also find the coordinates of point of division

Answer 1

Answer:

Step-by-step explanation:

Hope it helps you

Answer 2

Answer:

The ratio is 4 :7.

The coordinate of point of division is $(\frac{46}{11},0)$

Step-by-step explanation:

Given : Line segment joining the points (6,4)and(1,-7) is divided by x axis.

To find : The ratio in the line segment and the coordinates of point of division?

Solution :

Let the line segment points A=(6,4) and B=(1,-7)

Let the line segment divide by x-axis with point P=(x,0)

Let the ratio in which line segment divide be m:n=k : 1

Applying section formula,

$(x,y)=(\frac{a_2m+a_1n}{m+n}, \frac{b_2m+b_1n}{m+n})$

$a_1=6,b_1=4,a_2=1,b_2=-7,m=k,n=1$

Substitute the values,

$(x,0)=(\frac{1(k)+6(1)}{k+1}, \frac{-7(k)+4(1)}{k+1})$

$(x,0)=(\frac{k+6}{k+1}, \frac{-7k+4}{k+1})$

Compare the y-coordinate,

$\frac{-7k+4}{k+1}=0$

$-7k+4=0$

$7k=4$

$k=\frac{4}{7}$

So, The ratio is 4 :7.

Compare the x-coordinate,

$\frac{k+6}{k+1}=x$

Put the value of k,

$x=\frac{(\frac{4}{7})+6}{(\frac{4}{7})+1}$

$x=\frac{\frac{46}{7}}{\frac{11}{7}}$

$x=\frac{46}{11}$

So, The coordinate of point of division is $(\frac{46}{11},0)$