Question

find the ratio in which line 2 X + 3 Y - 5 is equal to zero divide 3 line segment joining(8, - 9) and (2, 1) also find the co-ordinate of the point of division...
Fast please

Answer 1

Let the line 2x+3y-5=0 divides line segment joining (8,-9) and (2,1) in the ratio k:1
Let the point of intersection be (m,n)
By section formula
m=2k+8/k+1
n=k-9/k+1
therefore m and n will lie on 2x+3y-5=0
So, 2(2k+8)/k+1+3(k-9)/k+1-5=0
4k+3k-5k+16-27+5=0
2k-16=0
k=16/2
k=8
Therefore the ratio of division is8:1
x=24/9 and y= -1/9