Are the points (2, 1) and (–3, 5) on the same or opposite side of the line 3x – 2y + 1 = 0?
Let f(x, y) ≡ 3x – 2y + 1
Therefore, the two points are on the opposite sides of the given line.
Find the equation of the straight line on which the perpendicular from origin makes an angle of 30o 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 3x + 4y + 7 = 0 and 4x – 3y + 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 2x – 3y + 9 = 0 measured along the line 2x – 2y + 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 15o. 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 2x + y + 2 = 0?