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: