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  • Find the ratio in which the segment joining the points (1,-3) and (4,5) is divided by x-axis? also find the coordinates of this point on x-axis.    

Find the ratio in which the segment joining the points (1,-3) and (4,5) is divided by x-axis? also find the coordinates of this point on x-axis.

 

 

Answers (1)

Using section formula point P(x,y) divides the line with endpoints A(x_1,y_1) \: \: \and\: \: B(x_2,y_2) in the ratio of  m:n then the coordinates of points x and y are calculated through the below written formula.

x=\frac{mx_2+nx_1}{m+n}\: and\: y=\frac{my_2+ny_1}{m+n}

The segment is divided by the X-axis. Thus the point at X-axis = (X,0)

Lets assume the ratio of segment AB = m:1 

So, O=\frac{\left (5m \right )+\left ( -3 \right )}{m+1}

m=\frac{3}{5}

Hence tthe ratio in which segment joining is 3:5

Using this ratio 

x=\frac{3\left ( 4 \right )+5\left ( 1 \right )}{3+5}= \frac{17}{8}

Hence the coordinates of X are \left ( \frac{17}{8}, 0 \right )

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Safeer PP

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