Question 11: Find the equation of the line which is perpendicular to the line
at the point where this line meets
.
Answer:
Slope of line
is
Therefore slope of line perpendicular to given line
Therefore the equation of line passing through (0,b) and having slope of is:
Question 12: are the vertices of a triangle
. Find:
(i) The equation of the median of triangle through vertex
(ii) The equation of altitude of triangle through vertex
Answer:
Mid point of
Therefore the equation of median of through
is
(i)
(ii) Slope of
Slope of line perpendicular to
Therefore the equation of altitude of through
Question 13: Determine whether the line through points is perpendicular to the line
. Does line
bisect the line segment joining the two given points?
Answer:
Slope of line passing through and
Slope of is
Slope of perpendicular
Therefore line passing through and
is perpendicular to
Mid point of and
Substituting in
we get that it satisfies the equation. Therefore
bisects the line joining
and
Question 14: Given a straight line . Determine the equation of the other line which is parallel to its and passes through
.
Answer:
Given
Slope of this line
Equation of line with slope and passing through
is
Question 15: Find the value of such that the line
is:
(i) Perpendicular to the line
(ii) Parallel to it.
Answer:
Given
Slope of this line
Slope of line is
Slope of line perpendicular to this line
(i) If perpendicular
(ii) If parallel
Question 16: The vertices of a triangle are
. Write down the equation of
. Find:
(i) The equation of the line through and perpendicular to
.
(ii) The co-ordinates of the point , where the perpendicular through
, as obtained in (i.), meets
.
Answer:
(i) Slope of
Slope of line perpendicualr to
Therefore equation of line passing through with slope
is:
… … … … (i)
(ii) Equation of
… … … … (ii)
Solving (i) and (ii) we get and $latex y = 1 &s=0$.
Therefore is
Question 17: 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 18: 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 19: are vertices of a triangle
. If
is the mid-point of
, use co-ordinate geometry to show that
is parallel to
. Give a special name to quadrilateral
.
Answer:
Coordinates of
Coordinates of
Slope of
Slope of
Therefore .
is a trapezoid.
Question 20: A line meets the
at point
and
at point
. The point
divides the line segment
internally such that
. Find:
(i) The co-ordinates of .
(ii) Equation of the line through and perpendicular to
.
Answer:
(i) Let and
Therefore
Similarly,
Therefore and
(ii) Slope of
Slope of line perpendicular to
Therefore the equation of line passing through with slope
: