Question 1: Point divides the line segment joining the points in the Find the co-ordinates of point Also, find the equation of the line through and parallel to

Answer:

divides in the

Therefore

Therefore the required equation is

Question 2: The line segment joining the points is divided in the at point in it. Find the co-ordinates of Also, find the equation of the line through and perpendicular to the line

Answer:

in the

Therefore the required equation is

Question 3: A line meets at point Find the co-ordinates of point Find the equation of a line through and perpendicular to

Answer:

At

Therefore the coordinate of

Therefore the slope of a like perpendicular to this line

Hence the line passing through

Question 4: Find the value of for which the lines are perpendicular to each other. **[2003]**

Answer:

Question 5: 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 co-ordinates of

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

Answer:

The equation of the line:

Question 6: are the co-ordinates of vertices respectively of rhombus Find the equations of the diagonals

Answer:

Equation of :

:

Question 7: Show that can be vertices of a square. Find the coordinates of its fourth vertex , if is a square. Without using the coordinates of vertex , find the equation of side of the square and the equation of diagonal

Answer:

In a square, the diagonals bisect each other. Therefore

:

:

Question 8: A line through origin meets the line at right angles at point find the coordinates of point

Answer:

.. … … … (i)

The equation of a line passing through and having slope is

.. … … … (i)

Solving equations (i) and (ii)

Question 9: A straight line passes through the point and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.

Answer:

Let y-intercept be and x-intercept be

is the Therefore:

Equation of line:

Question 10: Find the equation of the line passing through the point of intersection of ; and perpendicular to the line

Answer:

Solve equations

.. … … … (i)

.. … … … (ii)

Multiply (i) by 4 and (ii) by 3 and then add the equations, we get

in (i) we get

Therefore the intercept is

Hence the equation of the perpendicular:

Question 11: Find the equation of the line which is perpendicular to the line at the point where this line meets

Answer:

Question 12: are the vertices of a triangle Find:

(i) The equation of the median of triangle through vertex

(ii) The equation of altitude of triangle through vertex

Answer:

Therefore the equation of median of through is

Therefore the equation of altitude of through

Question 13: Determine whether the line through points is perpendicular to the line Does line bisect the line segment joining the two given points?

Answer:

Therefore line passing through is perpendicular to

in we get that it satisfies the equation. bisects the line joining

Question 14: Given a straight line Determine the equation of the other line which is parallel to its and passes through

Answer:

Equation of line with slope and passing through is

Question 15: Find the value of such that the line is:

(i) Perpendicular to the line (ii) Parallel to it.

Answer:

(i) If perpendicular

(ii) If parallel

Question 16: The vertices of a triangle are Write down the equation of Find:

(i) The equation of the line through and perpendicular to

(ii) The coordinates of the point , where the perpendicular through , as obtained in (i.), meets

Answer:

Therefore equation of line passing through with slope is:

.. … … … (i)

(ii) Equation of

.. … … … (ii)

Solving (i) and (ii) we get

Question 17: From the given figure, find:

(i) The co-ordinates of

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

Answer:

The equation of line parallel to and passing through

Question 18: are the vertices of triangle Write down the equation of the median of the triangle through **[2005]**

Answer:

Therefore equation passing through is

Question 19: are vertices of a triangle If is the mid-point of , use co-ordinate geometry to show that is parallel to Give a special name to quadrilateral

Answer:

is a trapezoid.

Question 20: A line meets the at point at point The point divides the line segment internally such that Find:

(i) The co-ordinates of

(ii) Equation of the line through and perpendicular to

Answer:

Similarly,

Slope of line perpendicular to

Therefore the equation of line passing through with slope :

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

Question 23: The given figure (not drawn to scale) shows two straight lines If equation of the line and equation of Write down the inclination of lines ; also, find the angle between **[1989]**

Answer:

Question 24: Write down the equation of the line whose gradian is and which passes through , where divides the line segment joining in the **[2001]**

Answer:

divides the line segment joining in the

Let the coordinates of

Therefore

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

Answer:

Equation of line passing through

Therefore if , then

Therefore the point is

Question 26: Point have co-ordinates respectively. Find:

(i) The

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

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

Answer:

Therefore equation of line passing through and slope is

Question 27: are two points on the respectively. is the mid-point of Find the

(i) Co-ordinates of

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

Answer:

is the mid point

(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 **[2010]**

Answer:

For point of intersection solve

Therefore equation of line

Question 29: is a parallelogram where Find: (i) Co-ordinates of (ii) Equation of diagonal **[2011]**

Answer:

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

(ii) Equation of

Question 30: Given equation of line

(i) Write the is the bisector of angle

(ii) Write the co-ordinates of point

(iii) Find the equation of

Answer:

Therefore slope

(iii) Equation of line