question_answer

In what ratio, the line made by joining the points \[A\,\,(-\,\,4,-\,3)\]and \[B\,\,(5,2)\]intersects X-axis?

A) \[3:2\]

B) \[2:3\]

C) \[-\,\,3:2\]                      

D) \[-\,\,2:3\]

Correct Answer: A

Solution :

Let C be the point on X-axis, where the line joining the points A and B intersect X-axis.

Let the ratio be k: 1.

Then, by section formula,

\[x=\frac{5k-4}{k+1}\]and \[0=\frac{2k-3}{k+1}\]

\[\Rightarrow \]   \[k=\frac{3}{2}\]

\[\therefore \]Required ratio \[=3:2\]