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 and
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:
Slope of
Slope of
Therefore
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
Let the coordinates of
Therefore
Equation of a line passing through with slope
Question 5: Point have co-ordinates
respectively. Find:
(i) The slope of
(ii) The equation of perpendicular bisector of the line segment
(iii) The value of lies on it [2008]
Answer:
(i) Slope of
(ii) Mid point of
Therefore equation of line passing through and slope
is
(iii) lies on it
Therefore
Question 6: are two points on the
respectively.
is the mid-point of
. Find the
(i) Co-ordinates of
(ii) Slope of line
(iii) Equation of line [2010]
Answer:
Let and
is the mid point
(i) Therefore
Hence and
(ii) Slope of
(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 and
[2010]
Answer:
(i) Slope
(ii) Slope of perpendicular
For point of intersection solve and
and
Therefore intersection
Therefore equation of line
Question 8: is a parallelogram where
. Find:
(i) Co-ordinates of
(ii) Equation of diagonal [2011]
Answer:
(i) Mid point of
Therefore we have
and
is the mid point of
as well (diagonals of a parallelogram bisect each other)
Hence
and
Hence
(ii) Equation of
Question 9: From the given figure, find:
(i) The co-ordinates of .
(ii) The equation of the line through and parallel to
. [2004]
Answer:
Slope of
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:
Mid point of
Therefore equation passing through and
is
Question 11: Find the value of for which the lines
and
are perpendicular to each other. [2003]
Answer:
Slope of
Slope of
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 line
The co-ordinates of
The co-ordinates of [2003]
Answer:
The equation of the line:
The and the
The coordinate of
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:
Slope of
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 co-ordinates of
. Calculate the area of triangle
, where
is origin. [1995]
Answer:
i) Given Point
Given equation is
Therefore slope of the new line
Equation of a line with slope and passing through
is
ii) Equation of is
When . Therefore
When . Therefore
Area of the triangle
sq. units.
Question 17: Find the value of a for the points are collinear. Hence, find the equation of the line. [2014]
Answer:
Given points
Slope of
Slope of
Because are collinear:
Question 18: In, . Find the equation of the median through
. [2013]
Answer:
Let be the mid point of
. Therefore the coordinates of
are
Slope of
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 co-ordinates of [2012]
Answer:
Given points
Slope
Equation of line:
When
Hence the co-ordinates of
Question 20: are vertices of a triangle
. Find:
i) The co-ordinates of the centroid of a triangle .
ii) The equation of a line through the centroid and parallel to . [2002]
Answer:
Let be the centroid. Therefore the coordinates of
are:
Slope
Therefore the equation of a line parallel to will pass through
Equation of the line: