What are the coordinates of a point that is 1/4th of the way from point A (0,0)and B(5,4)

Answer 1

You may use the distance formula to determine the distance from point A to point B, then find the x and y coordinates that have the desired distance from point (0,0) to that point.

OR ...

You may realize that th desired x coordinate is the x coordinate of A plus 1/4 of the difference between x coordinates; the same is true for the desired y coordinate.

The desired point has coordinates:

( (1/4)(5-0). (1/4)(4,0) )

( 5/4, 1 )

Answer 2

Let this point P(x, y). Then AP = <x, y> = 1/4AB = 1/4<5,4>;. From here x = 5/4, y = 4/4 = 1.

P(5/4, 1)