Question

Which of the following points lie on the same side of origin with respect to the line

x - 3y + 7 = 0?

• A. (9, 3)
• B. (3, 9)
• C. (3, -9)
• D. (-9, -3)

Answer 1

Answer: (A), (C)

The correct options are
A

(9, 3)

C

(3, -9)

Two points lie on the same side of a given straight line if we get same sign after substituting those points in the given s+ line.

We want to find the points which lie on the side of origin.

(0, 0) $\to$ 0 - 3 $\times$ 0 + 7 = 7 $\Rightarrow$ +ve,

So we will look for points which gives positive sign

(A)(9, 3) $\to$ 9 - 3 $\times$ 3 + 7 = 7 = 7 +ve

$\Rightarrow$ (9, 3) lies on the same side of origin.

(B)(3, 9) $\to$ 3 - 3 $\times$ 9 + 7 $\Rightarrow$ -ve

$\Rightarrow$ (3, 9) lies on the opposite side

(C)(3,-9) $\to$ 3 - 3 $\times$ 9 + 7 $\Rightarrow$ +ve

$\Rightarrow$ (3, -9) lies on the same side

(D)(-9, -3) $\to$ 3 $\times$ -9 - 3 $\times$ -3 + 7 $\Rightarrow$ -ve

$\Rightarrow$ (-9, -3) lies on the opposite side

$\Rightarrow$ A, C lie on the same side