Question

PLEASE HELP, I need to get this assignment done soon

The end points of AB are A(1, 4) and B(6, -1). If point C divides AB in the ratio of 2:3, the coordinates of C are ? If point D divides AC in the ratio of 3:2, the coordinates of D are ?

Answer 1

The distance from x=1 to x=6 is 5.  That from y=4 to y=-1 is also 5.

We find the coordinates of C separately.

Knowing that C divides AB in the ratio of 2:3, we know that the first part of the line connecting A to B is  

      2          2
---------- = ---- of the total x-distance from A to B, which is 5.  Thus, we get
  2 + 3       5                 (2/5)(5), or 2.  Add this 2 to the x-coordinate of A:
                                    1+2 = 3.  This is the x-coord. of C

      2          2
---------- = ---- of the total y-distance from A to B, which is 5.  Thus, we get
  2 + 3       5                 (2/5)(5), or 2.  Subtract this 2 from the y-coordinate of                                         A:   4-2, or 2.  The y-coord. of C is thus 2.
                                    1+2 = 3.  This is the x-coord. of C

The coordinates of C are (3, 3).

It would probably help you if you were to draw line AB and also plot C.  Once you have point A, you obtain the coord. of point C by adding 2 to the x-coord. of A, and subtracting 2 from the y-coord. of A (subtracting because the y-coordinate of A decreases as we move from A to B).