Question

Find the ratio in which the line segment joining the points A(3,-6) and B(5,3) is divided by x axis

Answer 1

Let the point of division be (x,0) and let the ratio be k:1

By using section formula , we get

(x,0) = (5k+3/k+1 , 3k-6/k+1 )

comparing y coordinateswe get

3k-6/k+1 = 0

3k-6 =0

3k=6

k=2

therefore ratio =2:1

comparing the x coordinates we get

x = 5k+3/k+1

subtituting k=2 ,we get

x=10 +3/2+1

x=13/3

therefore the points of intersection are (13/3 ,0)

it is from meritnation. Com
hope it helps

Answer 2

Step-by-step explanation:

Let A and B be divided in the ratio k:1, by point P(x,0) here, y=0 because P lies on X-axis.

ATQ:-

By section formula--  P(X,0) = (5k+3/k+1, 3K-6/K+1)

Now, if you compare Y(=0) and 3k-6/k+1 (we can equate them beacuse both of them are the values for Y)

⇒ 0= 3K-6/K+1

⇒ 0 X K+1= 3K-6

⇒ 0= 3K-6

⇒ 6= 3K

⇒ 2= K

Thus, your ratio is 2:1

hope it helped!