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 :