## Question

Are the points (2, 1) and (–3, 5) on the same or opposite side of the line 3*x* – 2*y* + 1 = 0?

### Solution

Let *f*(*x*, *y*) ≡ 3*x* – 2*y* + 1

.

Therefore, the two points are on the opposite sides of the given line.

#### SIMILAR QUESTIONS

Find the equation of the straight line on which the perpendicular from origin makes an angle of 30^{o} with x-axis and which forms a triangle of area sq. units with the coordinates axes.

Find the measure of the angle of intersection of the lines whose equations are 3*x* + 4*y* + 7 = 0 and 4*x* – 3*y* + 5 = 0.

Find the angle between the lines

where *a* > *b* > 0.

The slope of a straight line through *A*(3, 2) is 3/4. Find the coordinates of the points on the line that are 5 units away from *A*.

Find the direction in which a straight line must be drawn through the point (1, 2) so that its point of intersection with the line

*x* + *y* = 4 may be at a distance from this point.

Find the distance of the point (2, 3) from the line 2*x* – 3*y* + 9 = 0 measured along the line 2*x* – 2*y* + 5 = 0.

The line joining the points *A*(2, 0) and *B*(3, 1) is rotated about *A* in the anticlockwise direction through an angle of 15^{o}. Find the equation of the line in the new position. If *B* goes to *C* in the new position, what will be the coordinates of *C*?

The centre of a square is at the origin and one vertex is *A*(2, 1). Find the coordinates of other vertices of the square.

The extremities of the diagonal of a square are (1, 1), (–2, –1). Obtain the other two vertices and the equation of the other diagonal.

Is the point (2, –7) lie on origin side of the line 2*x* + *y *+ 2 = 0?