Question

the ratio in which the line segment joining ( 9, 7 ) and ( 5 , -3 ) is divided by the x axis is​

Answer 1

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Answer 2

Given,

The starting coordinates of the line segment$\[ = \left( {9,7} \right)\]$

The ending coordinates of the line segment$\[ = \left( {5, - 3} \right)\]$

To find,

The ratio in which the x-axis divides the given line segment.

Solution,

Know that the coordinate of the point that divides the line segment constructed by points $\[\left( {{x_1},{y_1}} \right)\]$ and $\[\left( {{x_1},{y_2}} \right)\]$ in the ratio $\[m:n\]$ is given as $\[\left( {\frac{{m{x_2} + n{x_1}}}{{m + n}},\frac{{m{y_2} + n{y_1}}}{{m + n}}} \right)\]$.

Know that on the x-axis the value of the y-coordinate is zero.

Refer to figure.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{{k \times - 3 + 1 \times 7}}{{k + 1}} = 0\\ \Rightarrow - 3k + 7 = 0\\ \Rightarrow k = \frac{7}{3}\end{array}\]$

Hence, the ratio in which the x-axis divides the given line segment is $\[7:3.\]$