Question

Determine the ratio in which the line 2x+y-4 = 0 divides the line segment joining the
(2-2) and (3,7)
​

Answer 1

Answer:

2:9 is the ratio

Step-by-step explanation:

Using 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)=(mx2+nx1/m+n, my2+ny1/m+n)

Now, let the ratio be k:1

Substituting (x1, y1)=(2,−2) and (x2, y2)=(3,7) in the formula, we get (k(3)+1(2)/k+1, k(7)+1(−2)/k+1)=(3k+2/k+1, 7k−2/k+1)

Since 2x+y−4=0 divides the line at P, this point will lie on the

2(3k+2/k+1)+ (7k−2/k+1) −4=0

6k+4+7k−2−4k−4=0

9k=2

k= 9/2

Hence, the ratio is 2:9

HOPE IT HELPS YOU

Answer 2

Answer:

use the formula

!(ax1+by1+c))!/((√(a^2+b^2))):!(ax2+bx2+c)!/(√(a^2+b^2))

so answer is

|2*2-2-4|/√(4+1):|2*3+7-4|/√(4+1)

|4-6|:|13-4|

2:9