Question

find the ratio in which the line segment joining the points A 2, - 2 and b 3, 7 is divided by the line 2 X + Y - 4 equal to zero

Answer 1

solve kar liyo aage okk

Answer 2

Answer:

The line segment joining the points A(2, - 2) and B(3, 7) is divided by the line 2x+y-4=0 in 2:9.

Step-by-step explanation:

Let the line segment joining the points A(2, - 2) and B(3, 7) is divided by the line 2x+y-4=0 in k:1.

Using section formula the point of intersection is

$P(x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$P(x,y)=(\frac{k(3)+1(2)}{k+1},\frac{k(7)+1(-2)}{k+1})$

$P(x,y)=(\frac{3k+2}{k+1},\frac{7k-2}{k+1})$

Since the intersection point lies on the line 2x+y-4=0, therefore the equation of line must be satisfied by the intersection point.

$2(\frac{3k+2}{k+1})+(\frac{7k-2}{k+1})-4=0$

$2(3k+2)+(7k-2)-4(k+1)=0$

$6k+4+7k-2-4k-4=0$

$9k-2=0$

$k=\frac{2}{9}$

Therefore the line segment joining the points A(2, - 2) and B(3, 7) is divided by the line 2x+y-4=0 in 2:9.