question_answer

Find the ratio in which y-axis divides the line segment joining the points \[A(5,-6)\] and \[B(-1,-4)\]. Also find the coordinates of the point of division.

Answer:

Let the required ratio be \[k:1\] and point on y-axis be (0, y)

\[\therefore \,AP:PB=k:1\]

Then, by section formula

\[\frac{5-k}{k+1}=0\]

\[5-k=0\]

\[\Rightarrow k=5\]

Hence, required ratio is \[5:1\]

\[\therefore y=\frac{(-4)(5)+(-6)(1)}{5+1}\]

\[\therefore y=\frac{-26}{6}=-\frac{13}{3}\]

Hence, point on y-axis is \[\left( 0,\frac{-13}{3} \right)\]