Question

The position of the point $(8,-9)$ with respect to the lines $2x+3y-4=0$ and $6x+9y+8=0$ is-

• A. point lies on the same side of the lines
• B. point lies on one of the lines
• C. point lies on the different sides of the line
• D. point lies between the lines

Answer 1

The correct option is A point lies on the same side of the lines

$L1=2x+3y-4=0$

$L2=6x+9y+8=0$

$L1$ & $L2$ are parallel to each other.

The position of the point $(8,-9)$ with respect to $L1$ is given by

$=2\times 8+3(-9)-4$

$=16-27-4$

$=16-31=-15<0$

Similarly, for the second line $\left(L2\right)$ substituting $x=8$ and $y=-9$,

we get

$6\times 8+9\times -9+8=48+8-81=56-81=-25<0$

If we plot the lines on the graph paper, the point lies on the same side of the lines.