Question

The ratio in which y - x + 3 = 0 divides the line
joining (4, -1) and (5, 6) is
(1) 2:1
(2) 3:2
(3) 1:2
(4) 4:1​

Answer 1

1:2

Step-by-step explanation:

if x = 0 then y = -3 & if y = 0 then x = 3

use section formula:

3 = m×5 + n×(4)/(m + n)

3m + 3n = 5m +4n

2m = n => m : n = 1 : 2

option (3) is correct

Answer 2

$\sf{\green{\huge{\underline{Straight\:Lines}}}}$

Let ratio be m : n.

$\boxed{\red{\mathsf{{\dfrac{m}{n}}\:=\:-{\dfrac{ax_1\:+\:by_1\:+\:c}{ax_2\:+\:by_2\:+\:c}}}}}$

• Note : Minus sign is used when points are on the same side of the line otherwise we take positive m/n.

$\mathsf{{\dfrac{m}{n}}\:=\:-{\dfrac{4\:+\:1\:-\:3}{5\:+\:-6\:-\:3}}}$

$\Rightarrow{\mathsf{\bold{{\dfrac{m}{n}}\:=\:{\dfrac{1}{2}}}}}$