Question

Find the ratio in which the straight line 2x +3y-20 divides the join of the points (2,3) and(2,10)

Answer 1

Answer:

Given the equation of line

2x+3y−20=0

Let A(2,3) and B(2,10) be the points

Let the point of division be of the form K:1 = m:n

Now

$x = \frac{mx2 + nx1}{m + n}$

$x = \frac{k \times 2 + 1\times 2}{k + 1}$

Similarly

$y = \frac{k \times 10 + 1 \times 3}{k + 1}$

Substitute (x,y) in the equation

2x +3y-20 =0

2(2k+2) +3(10k+3)= 20(k+1)

4k + 4 + 30k + 9 = 20k + 20

34k + 13 = 20k + 20

14k = 7

k = 1/2

∴ K:1=1:2=m:n