Question 1: Determine the distance between the following pair of parallel lines :

(i) and (ii) and

(iii) and (iv) and

Answer:

(i) Given parallel lines: and

Let be the distance between the given parallel lines.

units

(ii) Given parallel lines: and

Let d be the distance between the given parallel lines.

units

(iii) Given parallel lines: and

Let d be the distance between the given parallel lines.

units

(iv) Given parallel lines: and

Let d be the distance between the given parallel lines.

units

Question 2: The equations of two sides of a square are and Find the area of the square.

Answer:

Given parallel lines: and

Let d be the distance between the given parallel lines.

units

Therefore the area of the square sq. units.

Question 3: Find the equation of two straight lines which are parallel to and at unit distance from the point .

Answer:

The given line: … … … … … i)

Equation of a like parallel to line i) is … … … … … ii)

Line ii) is at a unit distance from point . Therefore,

or

Hence the required lines are and

Question 4: Prove that the lines and are equidistant from the line .

Answer:

Let is the distance between and

Let is the distance between and

Therefore the lines and are equidistant from the line as

Question 5: Find the equation of the line mid-way between the parallel lines and .

Answer:

Given lines:

… … … … … i)

… … … … … ii)

Let the equation of the line midway between the two lines be

… … … … … iii)

Distance between [i) and iii)] and [ii) and iii)] is equal.

Equation of the required line is

Question 6: Find the ratio in which the line divides the distance between the lines and .

Answer:

The three lines are parallel lines are the slope of all the lines is same

Let is the distance between and

Let is the distance between and

Hence the ratio if

Therefore the line divides the distance between the lines and in the ratio of