Answer:
C (2, -1)
Step-by-step explanation:
C has the same x coordinate as A = 2
that eliminates A and B.
and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).
so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.
but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.
so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.
the y difference A to B is 2 - -6 = 8
the 5/3 split of 8 units is actually 5 and 3.
so, the y coordinate of D is -6 + 5 = -1
and C must have the same y coordinate.
therefore, it is proven that answer C (2, -1) is the right answer.
