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 and

Question 3: The given figure (not drawn to scale) shows two straight lines . If equation of the line and equation of is . Write down the inclination of lines ; also, find the angle between **[1989]**

Answer:

Slope of

Slope of

Therefore

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

Let the coordinates of

Therefore

Equation of a line passing through with slope

Question 5: Point have co-ordinates respectively. Find:

(i) The slope of

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

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

Answer:

(i) Slope of

(ii) Mid point of

Therefore equation of line passing through and slope is

(iii) lies on it

Therefore

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

(i) Co-ordinates of

(ii) Slope of line

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

Answer:

Let and

is the mid point

(i) Therefore

Hence and

(ii) Slope of

(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 and **[2010]**

Answer:

(i) Slope

(ii) Slope of perpendicular

For point of intersection solve and

and

Therefore intersection

Therefore equation of line

Question 8: is a parallelogram where . Find:

(i) Co-ordinates of

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

Answer:

(i) Mid point of

Therefore we have and

is the mid point of as well (diagonals of a parallelogram bisect each other)

Hence

and

Hence

(ii) Equation of

Question 9: 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 10: 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 11: Find the value of for which the lines and are perpendicular to each other. **[2003]**

Answer:

Slope of

Slope of

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 line
- The co-ordinates of
- The co-ordinates of
**[2003]**

Answer:

The equation of the line:

The and the

The coordinate of

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:

Slope of

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 co-ordinates of . Calculate the area of triangle , where is origin. **[1995]**

Answer:

i) Given Point

Given equation is

Therefore slope of the new line

Equation of a line with slope and passing through is

ii) Equation of is

When . Therefore

When . Therefore

Area of the triangle sq. units.

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

Answer:

Given points

Slope of

Slope of

Because are collinear:

Question 18: 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 19: 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 20: 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: