Question 1: Find the equation of a line whose: ,
Answer:
Since , the corresponding point on
Given Slope
Therefore
Required equation of the line:
Question 2: Find the equation of a line whose:
Answer:
Since , the corresponding point on
Therefore
Required equation of the line:
Question 3: Find the equation of the line whose slope is
and which passes through
.
Answer:
Therefore
Required equation of the line:
Question 4: Find the equation of the line passing through and makes an angle of
with the positive direction of
.
Answer:
Therefore
Required equation of the line:
Question 5: Find the equation of the line passing through:
i)
ii)
Answer:
i)
Slope
Required equation of the line:
ii)
Slope
Required equation of the line:
Question 6: The co-ordinates of two points are
respectively. Find:
i) The gradient of ;
ii) The equation of
iii) The co-ordinates of the point where intersects the
.
Answer:
are
respectively
Slope or PQ
Required equation of the line:
Question 7: The co-ordinates of two points are
. Find:
i) The equation of ;
ii) The co-ordinates of the point where the line intersect the
.
Answer:
are
Slope or AB
Required equation of the line:
Therefore when
Hence
Question 8: The figure given alongside shows two straight lines
intersecting each other at point
. Find the equations of
.
Answer:
Slope of
Slope of
Equation of
Equation of
Question 9: 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 10: The following figure shows a parallelogram
whose side
is parallel to the
, and vertex
. Find the equations of
.
Answer:
is parallel to
Slope of
Equation of
Slope of
Equation of
Question 11: Find the equation of the straight line passing through origin and the point of intersection of the lines and
Answer:
Solving and
we get
Hence point of intersection
Slope of
Slope of
Question 12: In triangle , the co-ordinates of vertices
are
respectively. Find the equation of median through vertex
. Also, find the equation of the line through vertex
and parallel to
.
Answer:
Let be the mid point of
. Therefore the coordinates of
are
Slope of
Equation of
Slope of
Equation of the line through vertex and parallel to
Question 13: have co-ordinates
respectively. Find the equation of the line through
and perpendicular to
.
Answer:
Slope of
Slope of line perpendicular to
Therefore the equation of line perpendicular to BC and passing through A:
Question 14: Find he equation of the perpendicular dropped from the point onto the line joining the points
.
Answer:
Slope of
Slope of line perpendicular to
Therefore the equation of line perpendicular to AB and passing through C:
Question 15: Find the equation of the line, whose:
i)
ii)
iii)
Answer:
i) Points given are
Slope
Equation of line:
ii) Points given are
Slope
Equation of line:
iii) Points given are
Slope
Equation of line:
Question 16: Find the equation of line whose slope is and
.
Answer:
Slope
, Intercept
Equation of the line:
Question 17: Find the equation of the line with and a point on it
Answer:
Given point are
Slope
Equation of the line:
Question 18: Find the equation of the line through and making an intercept of
on the
.
Answer:
Given point are
Slope
Equation of the line:
Question 19: Find the equations of the lines passing through point and equally inclined to the co-ordinate axes.
Answer:
Given
Slope
Equation of line:
Also Slope
Equation of line:
Question 20: 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 21: Write down the equation of the line whose gradient is -and which passes through point , where
divides the line segment joining
in the ratio
Answer:
Ratio:
Let the coordinates of the point
Therefore
Therefore
Equation of line:
Question 22: 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:
Question 23: are the vertices of a triangle
. Find the equation of a line through the vertex
and the point
in
; such that
.
Answer:
Ratio:
Let the coordinates of the point
Therefore
Therefore
Slope
Equation of the line: