Final answer:
The necessary statements to confirm that 'A is southwest to C' are 'A is two miles south of B' and 'C is two miles north of B', assuming the typo in the latter is corrected to include 'north'.
Step-by-step explanation:
To determine which of the statements a, b, c, and d are necessary to make the claim that 'A is southwest to C' true, one must consider the orientation and distance relationships between points A, B, C, and D. Statement c says 'C is two miles of B', which seems incomplete and likely to be a typo, but we can infer that it intends to say 'C is two miles north of B'. Combining statement a, 'A is two miles south of B', with the inferred statement c would result in point A being southwest of C, as moving south from B to get to A and north from B to get to C would mean A is southwest of C.
Even though statement d, 'D is north-west of A' suggests a position that is consistent with southwest directionality, this does not directly inform the relationship between A and C.
Therefore, the necessary statements to make the original claim true are:
- a. A is two miles south of B.
- c. C is two miles north of B (assuming the typo is corrected to include 'north').