A straight canal is at a distance of km from a city and the nearest path from the city to the canal is in the north-east direction. Find whether a village which is at 3 km north and 4 km east from the city lies on the canal or not. If not, then on which side of the canal is the village situated?
Let O(0, 0) be the given city and AB be the straight canal.
∴ Equation of AB
i.e., Equation of canal is
Let V be the given village, then V ≡ (4, 3)
Putting x = 4 and y = 3 in (i), then
Hence the given village V does not lie on the canal. Also if,
Hence the village is on that side of the canal on which origin or city lies.
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.
Are the points (2, 1) and (–3, 5) on the same or opposite side of the line 3x – 2y + 1 = 0?
Is the point (2, –7) lie on origin side of the line 2x + y + 2 = 0?
Find the general equation of the line which is parallel to
3x – 4y + 5 = 0. Also find such line through the point (–1, 2).