Question

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

Answer 1

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.

Answer 2

Answer:

⭐ Solution ⭐

✏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 point (x1,y1) and (x2,y2) in the ratio of m:n then,

➡ By using section formula:-

=> x = mx2-nx1/m-n

➡ Now,

=> 1 = 7m-5n/m-n

=> 7m - 5n = m - n

=> 7m-m = 5n-n

=> 6m = 4n

=> m/n = 4/6

=> m/n = 2/3

=> m:n = 2:3

✔ Hence, the answer is 2:3