Question

The position of the points $\left(3,4\right)$ and $(2,-6)$ with respect to the line $3x-4y=8$ are

• A. On the same side of the line
• B. On different side of the line
• C. One point on the line and the other outside the line
• D. Both points on the line

Answer 1

The correct option is B

On different side of the line

Explanation for the correct option:

Find the position of given points with respect to the line

In the question, two point $\left(3,4\right)$ and $(2,-6)$ and an equation of line $3x-4y=8$ is given.

Rewrite the given equation as follows:

$3x-4y-8=0...\left(1\right)$.

Substitute $(x,y)=(3,4)$ in the equation $\left(1\right)$.

$3\left(3\right)-4\left(4\right)-8<0$

Now, substitute $(x,y)=(2,-6)$ in the equation $\left(1\right)$.

$$\begin{gathered} =3\left(2\right)-4(-6)-8 \\ =6+24-8 \\ =22 \end{gathered}$$

The resultant is greater than zero.

Therefore, both the given points lie on the opposite sides of the given line.

Hence, option $B$ is the correct answer.