CBSE BoardEnglish MediumSTD 10MathsCo-ordinate Geometry2 Marks
Question
Write the ratio in which the line segment joining points $(2, 3)$ and $(3, -2)$ is divided by $x$-axis.
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Answer
Let $P(x, 0)$ be the point of intersection of $x$-axis with the line segment joining $A(2,3)$ and $B(3,-2)$ which divides the line segment $A B$ in the ratio $\lambda: 1$.
Now according to the section formula if point a point P divides be the point of intersection of x -axis with the line segment joining $A(2,3)$ and $B(3,-2)$
which divides the line segment $A B$ in the ratio a line segment joining $A\left(x_1, y_1\right)$ and $B\left(x_2, y_2\right)$ in the ratio $m$ : $n$ internally than,
$\text{P(x, y)}=\Big(\frac{\text{nx}_1+\text{mx}_2}{\text{m}+\text{n}},\frac{\text{ny}_1+\text{my}_2}{\text{m}+\text{n}}\Big)$
Now we will use section formula as,
$(\text{x},0)=\Big(\frac{3\lambda+2}{\lambda+1},\frac{3-2\lambda}{\lambda+1}\Big)$
Now equate the y component on both the sides,
$\frac{3-2\lambda}{\lambda+1}=0$
On further simplification,
$\lambda=\frac{3}{2}$So x-axis divides AB in the ratio $\frac{3}{2}.$
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