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

Answer:

Slope of line is

Therefore slope of line perpendicular to given line

Therefore the equation of line passing through (0,b) and having slope of is:

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:

Mid point of

Therefore the equation of median of through is

(i)

(ii) Slope of

Slope of line perpendicular to

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:

Slope of line passing through and

Slope of is

Slope of perpendicular

Therefore line passing through and is perpendicular to

Mid point of and

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

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

Answer:

Given

Slope of this line

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:

Given

Slope of this line

Slope of line is

Slope of line perpendicular to this line

(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 co-ordinates of the point , where the perpendicular through , as obtained in (i.), meets .

Answer:

(i) Slope of

Slope of line perpendicualr to

Therefore equation of line passing through with slope is:

… … … … (i)

(ii) Equation of

… … … … (ii)

Solving (i) and (ii) we get and $latex y = 1 &s=0$.

Therefore is

Question 17: 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 18: 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 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:

Coordinates of

Coordinates of

Slope of

Slope of

Therefore .

is a trapezoid.

Question 20: A line meets the at point and 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:

(i) Let and

Therefore

Similarly,

Therefore and

(ii) Slope of

Slope of line perpendicular to

Therefore the equation of line passing through with slope :