Pick out the points that lie on the same side of this line as P. Consider the line 2x − 3y + 1 = 0 and the point P = (1, 2). Pick out the
points that lie on the same side of this line as P.
(a) (−1, 0)
(b) (−2, 1)
(c) (0, 0)
From my point of view  the answer will be option (b) becoz  it is on the same line.
I don't know other option . I don't have any idea about other option.
if anybody help me , i would be very thankful to him...
 A: Roughly speaking, a line
$$ax+by+c=0$$
divides the plane into two parts.
In one part,
$$ax+by+c<0$$
and in the other part
$$ax+by+c>0$$
So two points $(p,q)$ and $(r,s)$ are one the same side if
$$(ap+bq+c)(ar+bs+c)>0$$
and on opposite sides if
$$(ap+bq+c)(ar+bs+c)<0$$
Here is a more "rigorous" proof using dot-product:
Let the line be
$$ax+by+c=0$$
and the two points be $A=(p,q)$ and $B=(r,s)$.
First the equation of the line passing through the two points is
$$(s-q)x+(p-r)y+(qr-ps)=0$$
The point of intersection of the two lines $C=(x,y)$ can be obtained to be
$$x=\frac{b(ps-qr)+c(p-r)}{a(r-p)+b(s-q)}$$
$$y=\frac{a(qr-ps)+c(q-s)}{a(r-p)+b(s-q)}$$
Now consider the vectors AC and BC. Find the dot product.
If the dot product is positive, AB are on the same side. If the dot product is negative, AB are on opposite sides.
The dot product is
$$(p-x)(r-x)+(q-y)(s-y)$$
After simplification, it can be shown that it depends on the sign of
$$S=(ap+bq+c)(ar+bs+c)$$
In conclusion, if $S>0$, then the two points are on the same side. If $S<0$, they are on opposite sides.
A: If you're unfamiliar with "plane splitting" problems like this, I suggest you plot the line on graph paper, and plot points (a) (b) and (c).
A 2D line splits the entire plane into two half-planes.  Shade the two half-planes using different colored pencils (or different hatching). 
What do all the points p = [ x, y]  ON the line share in common numerically?
The line equation, given in this form:
2x + -3y + 1 = 0
makes explicit what those special points on the line have in common numerically....if you plug the point p's [ x, y ] coordinate numbers into the line equation, if the point is truly on the line, then the left side will come out equal to 0. 
Now, pick a point CLOSE TO the line in the right half-plane. Calculate the left side of the equation. Is the result positive or negative? Write this quantity next to the point you chose.  Now choose a point on the left side of the line.  Calculate the equation's left side and label the point with the result.  
Keep picking points, running the calculation and labeling with the result, until you see the pattern.
