A segment with endpoints A (3, 2) and B (6, 11) is partitioned by a point C such that AC and BC form a 2:3 ratio. Find the x value for C.

A. 3.8
B. 3.9
C. 4.2
D. 4.3

Question

A segment with endpoints A (3, 2) and B (6, 11) is partitioned by a point C such that AC and BC form a 2:3 ratio. Find the x value for C.

A. 3.8
B. 3.9
C. 4.2
D. 4.3

campbell_st · Answer

There are a couple of things here... The point C can be between A and B or Exterior to AB... which will make a difference to the answer. 

I'll assume its interior

so the formula is if a point is between 2 others in a ratio m:n

then $$x = \frac{m x_{2} + nx_{1}}{m + n}$$

so in your question m = 2, n = 3

$$x_{2} = 6... and .... x_{1} = 3$$

substitute them and you'll get the answer

anonymous · Answer

@campbell_st  Thank you!