Question

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 coordinates of the point of division.

Answer 1

here is your answer hope it may helps you!!!

Answer 2

Answer:

The ratio is 1:1

x-coordinate is $\frac{-3}{2}$

Step-by-step explanation:

Given: The segment joining$A(x_1,y_1)=(1,-5)$ and point $B(x_2,y_2)=(-4,5)$  divided by the x-axis.

To find : In what ratio is the segment joining also find the coordinates of the point of division?

Solution :

Let the line AB divides by Point C in a ration k:1

Then, Using section formula

$(x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}$

Divided by the x-axis.

So, $y_3=\frac{y_1n+y_2m}{m+n}$

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

$-5+5k=0$

$5=5k$

$k=\farc{5}{5}$

$k=1$

Which means x axis will divide the line segment AB in a ratio 1:1, externally.

Therefore, The ratio is 1:1.

Now, to find x-coordinate,

$x_3=\frac{x_1n+x_2m}{m+n}$

$x_3=\frac{1(1)+(-4)(1)}{1+1}$

$x_3=\frac{1-4}{2}$

$x_3=\frac{-3}{2}$

Therefore, x-coordinate is $\frac{-3}{2}$