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Question

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

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Solution

Let ratio be k:1
Hence
m1=k,m2=1
Given
point A, x1=1,y1=5
point B, x2=4,y2=5
Given P lies on X-axis, then it's Y-coordinate must be zero.
x=x,y=0
Using section formula
y=m1y2+m2y1m1+m2
0=k×5+1×(5)k+1
0=5k5k+1
5k5=0
5k=5
k=1
Hence, k=1
Now,
x=m1x2+m2x1m1+m2
x=k×(4)+1×1k+1
x=1×(4)+1×11+1
x=32
Hence the coordinate of point P(x,0)=P(32,0)

1100611_1198416_ans_0cc343193bc64717b8e9b643117e9ce8.png

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