Question

Equation of line inclined at an angle of ${45}^o$ with positive $x-$axis and dividing the line joining the points $(3,-1)$ and $(8,9)$ in the ratio $2:3$ internally, is

• A. $x-y-2=0$
• B. $3x-3y+1=0$
• C. $\sqrt{3}x-\sqrt{3}y+2=0$
• D. None of these

Answer 1

The correct option is A $x-y-2=0$

Co-ordinates of the point dividing the line joining he points $(3,-1)$ and $(8,9)$ internally in the ratio $2:3$ is

$(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})=(\frac{2\left(8\right)+3\left(3\right)}{5},\frac{2\left(9\right)-3\left(1\right)}{5})=(\frac{25}{5},\frac{15}{5})=(5,3)$

The above point must satisfy the required equation $x-y-2=0=>5-3-2=0$

Therefore, required equation of the line is $x-y-2=0$