Question

The ratio in which the line segment joining a(6,3) and b( -2,-5) is divided by x axis

Answer 1

Since, the the line is divided by x-axis, y=0

Then,let the point dividing the line segment be

P(x, 0)

Now,let's the required ratio be k:1

Then, by section formula:

$\sf x=\frac{mx_2+nx_1}{m+n} →x=\frac{-2k+6}{k+1} \\\\\sf y=\frac{my_2+ny_1}{m+n}\:\:=\frac{-5k+3}{k+1}$

Now, we know that y=0

$\sf → 0=\frac{-5k+3}{k+1} \\ \sf</p><p>→ 0=-5k+3 \\ \sf</p><p>→ 3=5k\\ \sf</p><p>→k=3/5\\ \sf</p><p>So, \:the \:required \:ratio \:is\:\frac{3}{5} : 1$

So the ratio is 3:5