Explanation

Statement (1)

Since we have P and Q, we could find an equation for the line and determine whether R is on the line. This statement alone is sufficient. We do not need to actually find the equation or check point R.

The correct answer would be between A/D.

Statement (2)

A point equidistant from P and Q could lie anywhere on the perpendicular bisector of segment PQ (i.e. the perpendicular line passing through the midpoint of PQ). Point R could be on PQ (at the midpoint), but R could also be anywhere on the perpendicular bisector not on PQ. This statement alone is insufficient.

**The correct choice is A. **

Since we have P and Q, we could find an equation for the line and determine whether R is on the line. This statement alone is sufficient. We do not need to actually find the equation or check point R.

The correct answer would be between A/D.

Statement (2)

A point equidistant from P and Q could lie anywhere on the perpendicular bisector of segment PQ (i.e. the perpendicular line passing through the midpoint of PQ). Point R could be on PQ (at the midpoint), but R could also be anywhere on the perpendicular bisector not on PQ. This statement alone is insufficient.

The expression “mind your P’s and Q’s” (commonly used to mean “be on your best behavior”) has several possible origins.

It might have originated with printers telling their apprentices not to mix up the letter “p” with an upside down letter “q” when typesetting. Others think that the “p” stands for “please ” and “q” for a mispronunciation of “excuse me” or “thank you.”