Question

find the ratio in which the y axis divides the line segment joining the points (6 -4) and (-2 -7) also find the point of intersection

Answer 1

Answer:

But the point \(P\) lies on the line (1), so its coordinates satisfy eqaution (1).

\(\therefore\frac{\;6k-2}{k+1}-3\left(\frac{3k-5}{k+1}\right)=0\)

\(\Rightarrow\;6k-2-9k+15=0\)

\(\Rightarrow\;-3k=-13\)

\(\Rightarrow\;k=\frac{13}3\)

\(\therefore\;x=\frac{6k-2}{k+1}=\frac{6\times{\displaystyle\frac{13}3}-2}{{\displaystyle\frac{13}3}+1}=\frac{\displaystyle\frac{78-6}3}{\displaystyle\frac{13+3}3}=\frac{72}{16}=\frac92\)

and \(y=\frac{3k-5}{k+1}=\frac{3\times{\displaystyle\frac{13}3}-5}{{\displaystyle\frac{13}3}+1}=\frac{\displaystyle\frac{39-15}3}{\displaystyle\frac{13+3}3}=\frac{24}{16}=\frac32\)

and ratio is \(k:1\) i.e., \(\frac{13}3:1\) i.e., \(13:3\).

Hence, the given line divides the join of points \(A(-2,-5)\) and \(B(6,3)\) in the ratio \(13:3\) and point of intersection is \(P(\frac92,\frac32)\).