CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
MCQ
The ratio in which the $x-$ axis divides the segment joining $(3, 6)$ and $(12, -3)$ is :
✓
$2 : 1$
B
$1 : 2$
C
$-2 : 1$
D
$1 : -2$
✓
Answer
Correct option: A.
$2 : 1$
Let $P(x, 0)$ be the point of intersection of $x-$ axis with the line segment joining $A(3, 6)$ and $B(12, -3)$ which divides the line segment $AB$ in the ratio $\lambda:1.$
Now, according to the section formula if point a point $P$ divides 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,
$(\text{x},0)=\Big(\frac{12\lambda+3}{\lambda+1},\frac{-3\lambda+6}{\lambda+1}\Big)$
Now equate the $y$ component on both the sides,
$\frac{-3\lambda+6}{\lambda+1}=0$
On further simplification,
$\lambda=\frac{2}{1}$
So $, x-$ axis divides $AB$ in the ratio $\frac{2}{1}.$
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