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.
C ≡ (–2, –1) and D ≡ (1, –2)
(By special corollary (ii))
Now in triangle AOB,
âˆµ O is the mid-point of AC and BD
Find the equation of the straight line through the point P(a, b) parallel to the lines . Also find the intercepts made by it on the axes.
The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120o with the positive direction of y-axis. Find the equation of the 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 extremities of the diagonal of a square are (1, 1), (–2, –1). Obtain the other two vertices and the equation of the other diagonal.