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).
