Question 1: Find the slope and of the line:
Answer:
Question 2: The equation of a line is Find its slope and
Also, find its inclination.
Answer:
Question 3:
Answer:
Question 4: Find the slope of the line which is parallel to:
Answer:
Question 5: Find the slope of the line which is perpendicular to:
Answer:
Question 6:
i) Lines are parallel to each other. Find the relation connecting
ii) Lines are perpendicular to each other. Find the relation connecting
Answer:
Question 7: Find the value of if the lines, whose equations are
are perpendicular to each other.
Answer:
Question 8: The equation of a line
i) Find the slope of the line
ii) Calculate the angle that the line makes with the positive direction of the
Answer:
Question 9: The lines represented by are parallel. Find the value of
Answer:
Question 10: If the lines are perpendicular to each other, find the value of
[2006]
Answer:
Question 11: The line through is perpendicular to the line
Find the value of
[2012]
Answer:
Question 12: Find the equation of the line passing through and parallel to:
Answer:
i) Line parallel to has a
Equation of a line with and passing through
is
ii) Line parallel to has a
Equation of a line with and passing through
is
Question 13: 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
Equation of a line with and passing through
is
ii) Given Point
Equation of a line with and passing through
is
Question 14: Find the equation of the line passing through and perpendicular to
Answer:
Equation of a line with and passing through
is
Question 15: Find the equation of the perpendicular bisector of the line segment obtained on joining the points
Answer:
Let P be the bisector of the points
Let the coordinates of
Equation of a line with and passing through
is
Question 16: are the vertices of rhombus
Find the equations of the diagonals
Answer:
Equation of a line with and passing through
Question 17: are the vertices of a square
Find the equations of the diagonals
Answer:
Equation of AC :
Question 18: are the vertices of triangle
Find the equation of:
i) The median of the triangle through
ii) The altitude of the triangle through
iii) The line through and parallel to
Answer:
Equation of BD
Slope of line perpendicular to this
Equation of line
Slope of line parallel to this
Equation of line
Question 19: i) Write down the equation of the line , through
and perpendicular to the line
meets the
and the
at
write down the co-ordinates of
Calculate the area of triangle
, where
is origin. [1995]
Answer:
i) Given Point
Equation of a line with and passing through
ii) Equation of
Question 20: The line write the co-ordinates of
Determine the equation of the line through
and perpendicular to
Answer:
Given equation
When
Equation of a line with and passing through
Question 21: The point is the foot of perpendicular from
to the line whose equation
Determine:
i) The equation of the line ii) The co-ordinates of
Answer:
i)
Equation of AP with and passing through
ii) The coordinate of P is the intersection of the two lines:
Solving the two equations, we get
Question 22: The points respectively. Find the equations of
If
cuts the
at
cuts the
at
, find the co-ordinates of
Answer:
Question 23: Find the value of a for the points are collinear. Hence, find the equation of the line. [2014]
Answer: