Question

determine the ratio in which the line 2x+ y-4=0 divides the line segment joining the points A(2,-2) and B(3,7)

Answer 1

I don't know about this answer sorry

Answer 2

The given points are A(2,-2) and B(3,7)
first of all we will find the equation of the line
(y -y1) = (y2 - y1)/(x2 - x1) * (x - x1)
(y + 2) = (7+2)/(3-2) * (x - 2)
y + 2 = 9*(x - 2)
y + 2 = 9x - 18
9x - y - 20 = 0. ...........(1)
and the given eqution is
2x + y - 4 = 0. ............(2)
by solving equation (1) &(2) we have
x = 24/11
y = -4/11

so (24/11 , -4/11) is the point of intersection so this is the point which divides the line in a certain ratio

so by the section
x = (mx1 + nx2)/(m + n)
to calculate the ratio we need only one parameter
so let the ratio be k : 1
so by the section formula we have

24/11 = (k*2 + 3)/(k + 1)

on cross multiplication we have

24(k + 1) = 11(2k + 3)
24k + 24 = 22k + 33
24k - 22k = 33 - 24
2k = 9
k = 9/2
so the ratio will be
9/2:1
or we can say that
9:2
so the answer is 9:2
:-)