Question 1: A line intersects at point
and cuts off an intercept of
units from the positive side of
Find the equation of the line. [1992]
Answer:
Equation of line
Question 2: Find the equation of a line passing through the point and having the
of
units. [2002]
Answer:
Equation of line passing through
Question 3: The given figure (not drawn to scale) shows two straight lines
If equation of the line
is
and equation of
is
Write down the inclination of lines
; also, find the angle between
[1989]
Answer:
Question 4: Write down the equation of the line whose gradian is and which passes through
, where
divides the line segment joining
in the ratio
[2001]
Answer:
Given divides the line segment joining
in the ratio
Therefore
Question 5: Point have coordinates
respectively. Find:
(ii) The equation of perpendicular bisector of the line segment
(iii) The value of lies on it [2008]
Answer:
Question 6: are two points on the
respectively.
is the mid-point of
Find the
(i) coordinates of
(ii) Slope of line
(iii) Equation of line [2010]
Answer:
is the mid point
Hence
(iii) Equation of
Question 7: The equation of a line is Find:
(i) Slope of the line.
(ii) The equation of a line perpendicular to the given line and passing through the intersection of the lines [2010]
Answer:
For point of intersection solve
Therefore intersection
Therefore equation of line
Question 8: is a parallelogram where
Find:
(i) coordinates of
(ii) Equation of diagonal [2011]
Answer:
Hence
Equation of
Question 9: From the given figure, find:
(i) The coordinates of
(ii) The equation of the line through and parallel to
[2004]
Answer:
The equation of line parallel to and passing through
Question 10: are the vertices of triangle
Write down the equation of the median of the triangle through
[2005]
Answer:
Therefore equation passing through is
Question 11: Find the value of for which the lines
are perpendicular to each other. [2003]
Answer:
Since the two lines are perpendicular,
Question 12: A straight line passes through the points It intersects the co-ordinate axes at points
is the mid-point of the line segment
Find:
The equation of the line
The coordinates of
The coordinates of [2003]
Answer:
The equation of the line:
Question 13: If the lines are perpendicular to each other, find the value of
[2006]
Answer:
Given equation is
Given equation is
Since they are perpendicular,
Question 14: The line through is perpendicular to the line
Find the value of
[2012]
Answer:
Given equation is
Since they are perpendicular,
Question 15: i) Find the equation of the line passing through and parallel to
ii) Find the equation of the line parallel to the line and passing through the point
[2007]
Answer:
i) Given Point
Given equation is
Equation of a line with slope and passing through
is
ii) Given Point
Given equation is
Equation of a line with slope and passing through
is
Question 16: i) Write down the equation of the line , through
and perpendicular to the line
ii) meets the
and the
at
write down the coordinates of
Calculate the area of triangle
, where
is origin. [1995]
Answer:
i) Given Point
Given equation is
Equation of a line with slope and passing through
is
ii) Equation of is
When
When
Question 17: Find the value of a for the points are collinear. Hence, find the equation of the line. [2014]
Answer:
Given points
Because are collinear:
Question 18: In, Find the equation of the median through
[2013]
Answer:
be the
Therefore the coordinates of
are
Equation of
Question 19: The line through intersects
i) Write the slope of the line.
ii) Write the equation of the line.
iii) Find the coordinates of [2012]
Answer:
Given points
Slope
Equation of line:
When
Hence the coordinates of
Question 20: are vertices of a triangle
Find:
i) The coordinates of the centroid of a triangle
ii) The equation of a line through the centroid and parallel to [2002]
Answer:
be the centroid. Therefore the coordinates of
are:
Equation of the line: