In what ratio does the point (1, 12) divide the join of (5, 6) and (7,

1.	In what ratio does the point (1, 12) divide the join of (5, 6) and (7, 3)?
Answer» Let the POINT (1, 12) divide the line segment joining (5, 6) and (7, 3) in the ratio m : n. Here the point (1, 12) divides the line segment EXTERNALLY. If a point $(x,\ y)$ divides a line segment joining the points $(x_1,\ y_1)$ and $(x_2,\ y_2)$ in the ratio m : n externally, then by section formula, $\longrightarrow x=\dfrac{mx_2-nx_1}{m-n}$ So here, $\longrightarrow 1=\dfrac{7m-5n}{m-n}$ $\longrightarrow 7m-5n=m-n$ $\longrightarrow 6m=4n$ $\longrightarrow \dfrac{m}{n}=\dfrac{2}{3}$ $\longrightarrow\underline{\underline{m:n=2:3}}$ Hence 2:3 is the ANSWER.

In what ratio does the point (1, 12) divide the join of (5, 6) and (7, 3)?

Answer»

Let the POINT (1, 12) divide the line segment joining (5, 6) and (7, 3) in the ratio m : n.

Here the point (1, 12) divides the line segment EXTERNALLY.

If a point $(x,\ y)$ divides a line segment joining the points $(x_1,\ y_1)$ and $(x_2,\ y_2)$ in the ratio m : n externally, then by section formula,