Question 21: 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 22: Find the equation of a line passing through the point and having the of units.** [2002]**

Answer:

Equation of line passing through and

Question 23: 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 24: 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 25: The ordinate of a point lying on the line joining points . Find the co-ordinates of that point.

Answer:

Let the ordinate of a point lying on the line joining points be

Equation of line passing through and

Therefore if , then

Therefore the point is

Question 26: 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 27: 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 28: 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 29: 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 30: Given equation of line _{ }is .

(i) Write the slope of line _{ }is is the bisector of angle

(ii) Write the co-ordinates of point .

(iii) Find the equation of

Answer:

(i)

Therefore slope

(ii) Therefore

(iii) Equation of line