ADVANCED MATHEMATICS FORM 5 – COORDINATE GEOMETRY – part 2

IMPORTANT STEPS

1.      Get slope of formatted line i.e. and then use if to get slope of L₂. Since

2.      From equation of by using and point provided from.

3.      Get coordinate of the food by solving the equation and simultaneously as the way Y please.

EXAMPLE

1.      Find the acute angle 6. between lines

and

2.      Find the acute angle between the lines represented by

3.      find the equation of the line in which such that X – axis bisect the angle between the with line

4.      find the equation of perpendicular bisector between A and B

5.      Find the coordinate of the foot perpendicular from of the line

6.      Find the equation of the line parallel to the line 3x – 2y + 7 = 0 and passing through the point

7.      find the equation if the line perpendicular to the line and passing through the point

8.      Find the equation of perpendicular bisector of AB. where A and B are the point and respectively.

Solution

Given

        

Consider

From

Also

Recall

=

θ₂tan^-1 1
Therefore;

2)

Solution

Given

Factorize completely

From

 

Recall

    

Given

Consider the figure below

From

The slope is negative then at x –axis y=0

 

4) Solution

Given A B

From

Also

Midpoint =

M.p =

Then

The equation is

  

Solution

Given

From

But

For the equation

The coordinate of the foot is 

The perpendicular line from point A to the straight line intersect the line at point B. if the perpendicular is extended to C in such a way that AB = . Determine line coordinate of C.

Solution

Given

Let

From

Then

The coordinate of is since point B

Recall

Since

Then

For x

Compare off

∴

For y

The coordinate of C is