Question

Determine the ratio in which the line 2x + y - 4 =0 divide the line segment joining the points (- 4,3) and (6,3). Hence find the coordinates P​

please guys answer fast..!!

Answer 1

Answer:

Hence the line is divided in the ratio 2:9.

Step-by-step explanation:

Using the section formula, if a

point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Let the ratio be k:1 and P be the point where lines intersect.

Substituting (x1,y1)=(2,−2) and (x2,y2)=(3,7)  in the

section formula, we get  P=(k+1k(3)+1(2),k+1k(7)+1(−2))=(k+13k+2,k+17k−2)

Since 2x+y−4=0 divides the line at P, So the point P lie on this line, therefore we have

(k+13k+2)+k+17k−2−4=0

6k+4+7k−2−4k−4=0 

9k=2

k=92

Hence, the ratio is 2:9