Coordinate Geometry Part II
Example 1
A typical coordinate geometry question from the O Levels
![](//4.bp.blogspot.com/_kl5LiMhGUng/TGtbm9Mj3rI/AAAAAAAAAUE/Ub6iwuvPfgc/s400/18augA.png)
Given that AC = 3AB, find the coordinates of point B.
Remarks:
A lot of students will try to use the distance formula to form simultaneous equations in x and y to find the coordinates of B. This is a very long and tedious method. A much simpler method is to use ratio and proportion to find the coordinates of B
To find the x coordinate of B
![](//2.bp.blogspot.com/_kl5LiMhGUng/TGtqSeazmMI/AAAAAAAAAUM/v085XD9mAlw/s400/18augB.png)
We can use the same method to find the y coordinate of point B
![](//2.bp.blogspot.com/_kl5LiMhGUng/TGttUm7aA8I/AAAAAAAAAUU/-Zw4pOOfbdg/s400/18augC.png)
Therefore the coordinates of point B is (4,4)
A typical coordinate geometry question from the O Levels
![](http://4.bp.blogspot.com/_kl5LiMhGUng/TGtbm9Mj3rI/AAAAAAAAAUE/Ub6iwuvPfgc/s400/18augA.png)
Given that AC = 3AB, find the coordinates of point B.
Remarks:
A lot of students will try to use the distance formula to form simultaneous equations in x and y to find the coordinates of B. This is a very long and tedious method. A much simpler method is to use ratio and proportion to find the coordinates of B
To find the x coordinate of B
![](http://2.bp.blogspot.com/_kl5LiMhGUng/TGtqSeazmMI/AAAAAAAAAUM/v085XD9mAlw/s400/18augB.png)
We can use the same method to find the y coordinate of point B
![](http://2.bp.blogspot.com/_kl5LiMhGUng/TGttUm7aA8I/AAAAAAAAAUU/-Zw4pOOfbdg/s400/18augC.png)
Therefore the coordinates of point B is (4,4)
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