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