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

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:

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

Therefore

Question 5: Point have coordinates respectively. Find:

(ii) The equation of perpendicular bisector of the line segment

(iii) The value of lies on it **[2008]**

Answer:

Question 6: are two points on the respectively. is the mid-point of Find the

(i) coordinates of

(ii) Slope of line

(iii) Equation of line **[2010]**

Answer:

is the mid point

Hence

(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 **[2010]**

Answer:

For point of intersection solve

Therefore intersection

Therefore equation of line

Question 8: is a parallelogram where Find:

(i) coordinates of

(ii) Equation of diagonal **[2011]**

Answer:

Hence

Equation of

Question 9: From the given figure, find:

(i) The coordinates of

(ii) The equation of the line through and parallel to **[2004]**

Answer:

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:

Therefore equation passing through is

Question 11: Find the value of for which the lines are perpendicular to each other. **[2003]**

Answer:

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 the line

The coordinates of

The coordinates of **[2003]**

Answer:

The equation of the line:

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:

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 coordinates of Calculate the area of triangle , where is origin. **[1995]**

Answer:

i) Given Point

Given equation is

Equation of a line with slope and passing through is

ii) Equation of is

When

When

Question 17: Find the value of a for the points are collinear. Hence, find the equation of the line. **[2014]**

Answer:

Given points

Because are collinear:

Question 18: In, Find the equation of the median through ** [2013]**

Answer:

be the Therefore the coordinates of are

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 coordinates of **[2012]**

Answer:

Given points

Slope

Equation of line:

When

Hence the coordinates of

Question 20: are vertices of a triangle Find:

i) The coordinates of the centroid of a triangle

ii) The equation of a line through the centroid and parallel to **[2002]**

Answer:

be the centroid. Therefore the coordinates of are:

Equation of the line: