Note: The equation of a straight line passing through with the positive x-axis is given by , where is the distance of the point on the line from the point .

The coordinate of any point on the line at a distance from the point are .

Question 1: A line passes through a point and makes an angle of with the x-axis and intersects the line at the point . Find .

Answer:

… … … … … i)

From equation i)

Question 2: If the straight line through the point makes an angle with the x-axis and meets the line at , find the length .

Answer:

… … … … … i)

From equation i)

Question 3: A straight line drawn through the point, making an angle with positive x-axis intersects another line in the point . Find length .

Answer:

… … … … … i)

From equation i)

Question 4: A line drawn through parallel to the line . Find the coordinates of the two points on this line which are at a distance of units from .

Answer:

comparing with

Considering sign we get:

Hence the point is

Considering sign we get:

Hence the point is

Question 5: The straight line through inclined at an angle with the x-axis meets the line in . Find the length of .

Answer:

… … … … … i)

From equation i)

Question 6: Find the distance of the point from the line measured along a line making an angle of with the x-axis.

Answer:

… … … … … i)

From equation i)

Question 7: Find the distance of the point from the line measured parallel to a line having slope .

Answer:

… … … … … i)

From equation i)

Question 8: Find the distance of the point from the line measured parallel to a line having slope .

Answer:

… … … … … i)

From equation i)

Question 9: Find the distance of the point from the line measured parallel to the line .

Answer:

… … … … … i)

From equation i)

Question 10: Find the distance of the point from the line measured parallel to the line .

Answer:

… … … … … i)

From equation i)

Question 11: Find the distance of the line from the point in the direction of the line whose slope is .

Answer:

… … … … … i)

From equation i)

Question 12: A line is such that its segment between the straight line is bisected at the point . Obtain its equation.

Answer:

makes an angle with positive x-axis.

Therefore the coordinate of and coordinate of

We know

bisects

Therefore the equation of the line would be

Question 13: Find the equation of straight line passing through and having an intercept of length between the straight lines .

Answer:

makes an angle with positive x-axis.

Therefore the coordinate of and coordinate of

We know

We know

Squaring both sides

… … … … … ii)

From ii) either

Therefore the equation of line is

Therefore the equation of line is :