Question

38. The ratio in which the line segment joining A(6.3) and B(-2,-5) is divided by the
X-axis is
a. 2:3
b. 3:2
c. 3:5
d. 1:3​

Answer 1

Given ,

The line segment joining A(6,3) and B(-2,-5) is divided by the x axis

Let , the ratio in which x axis divides the line segment AB is m : n

We know that , the section formula is given by

$\boxed{ \tt{x = \frac{m x_{2} + n x_{1} }{m + n} \: \:, \: \: y= \frac{m y_{2} + n y_{1} }{m + n} }}$

And the coordinate of x axis = (x , 0)

Thus ,

$\tt \implies 0 = \frac{ - 5m + 3n}{m + n}$

$\tt \implies 5m = 3n$

$\tt \implies\frac{m}{n} = \frac{3}{5}$

Therefore , the correct option is C

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Answer 2

Given ,

The line segment joining A(6,3) and B(-2,-5) is divided by the x axis

Let , the ratio in which x axis divides the line segment AB is m : n

We know that , the section formula is given by

$\boxed{ \tt{x = \frac{m x_{2} + n x_{1} }{m + n} \: \:, \: \: y= \frac{m y_{2} + n y_{1} }{m + n} }} </p><p></p><p> </p><p> </p><p> </p><p>$

And the coordinate of x axis = (x , 0)

Thus ,

$\tt \implies 0 = \frac{ - 5m + 3n}{m + n}</p><p> \\ </p><p></p><p>\tt \implies 5m = 3n \\ </p><p></p><p>\tt \implies\frac{m}{n} = \frac{3}{5}$

Therefore , the correct option is C

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