Question 1: Determine the distance between the following pair of parallel lines :
(i)
(ii)
(iii)
(iv)
Answer:
(i) Given parallel lines:
Let be the distance between the given parallel lines.
(ii) Given parallel lines:
Let d be the distance between the given parallel lines.
(iii) Given parallel lines:
Let d be the distance between the given parallel lines.
(iv) Given parallel lines:
Let d be the distance between the given parallel lines.
Question 2: The equations of two sides of a square are Find the area of the square.
Answer:
Given parallel lines:
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
Question 4: Prove that the lines are equidistant from the line
.
Answer:
Let is the distance between
Let is the distance between
Therefore the lines are equidistant from the line
as
Question 5: Find the equation of the line mid-way between the parallel lines .
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
.
Answer:
The three lines are parallel lines are the slope of all the lines is same
Let is the distance between
Let is the distance between
Therefore the line divides the distance between the lines
in the ratio of