Question

an equation of a line whose segment between the coordinates axes is divided by the point (1/2,1/3)in the ratio 2:3
please answer it fast i will mark u as brainlist​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• Equation of the line is $\boxed{\bf{6x + 6y= 5}}$

☆ɢɪᴠᴇɴ☆

• Segment of a line between co-ordinate axes is divided by the point $(\frac{1}{2}, \frac{1}{3})$ in the ratio $2:3$.

★ᴛᴏ ғɪɴᴅ★

• Equation of the line.

⍟ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ⍟

• Let 'a' and 'b' be the x-intercept and y-intercept respectively of the line.

• Then the line pass through A(a, 0) and B(0, b) and AB is the line segment between the axes.

So,

$\:\:\:\:\:\:\:\:\:\:\: (\frac{2.0+3.a}{2+3}, \frac{2.b+3.0}{2+3}) = (\frac{1}{2}, \frac{1}{3})$

$\implies (\frac{3a}{5}, \frac{2b}{5}) = (\frac{1}{2}, \frac{1}{3})$

$\implies \frac{3a}{5} = \frac{1}{2}, \frac{2b}{5} = \frac{1}{3}$

$\implies a = \frac{5}{6}, b= \frac{5}{6}$

Using Intercept Form, equation of the line is given by,

$\:\:\:\:\:\:\:\:\:\:\: \frac{x}{a} + \frac{y}{b} = 1$

$\implies \frac{x}{\frac{5}{6}} + \frac{y}{\frac{5}{6}} = 1$

$\implies \frac{6x}{5} + \frac{6y}{5} = 1$

$\implies 6x + 6y= 5$