Point P is on segment ABOUT such that AP:PB Is 4:5. If A had coordinates (4,2) and B has coordinates (22,2), determine and state the coordinates of P

Question

It is a hard geometry topic that I never understand how to operate.

Answer 1

Since point A and point B have the same y coordinate,  this line is horizontal.   The point P will also have y coordinate of 2.   The remaining problem is to find the x coordinate of P. 

 

One way to do this is as follows.   

For some value of x, let   4x be the distance from A to P and 5x be the distance from  P to B.   This forces the ratio AP:PB to be 4:5 as required.  

Since the distance from A to B is 22-4 =18,      18 =  4x + 5x = 9x.    So x =2.  

This means that the distance from A to P  (which is 4x ) = 8.  

The x coordinate of P is then 4 + 8 = 12.  

  So P is  (12, 2)