Explanation

This question is asking us whether Point Q is equidistant from these other two points. If it is, then, possibly it lies on the middle point of the line segment connecting those two points. That line segment would lie along the horizontal line and it would have an x-value equidistant between 4 and -2, which would be 1. (You can find both values by calculating the average of the coordinates.) But this isn't the only point that is equidistant. You could convince yourself visually or by trying case of the distance formula / Pythagorean Theorem that any point that lies on the vertical line will be equidistant to the other two points. If the point is on that line, then the answer to the question will be definitively "yes." Let's move to the data statements, evaluating them separately first.

Statement (1) gives us what we just said: this is the exact condition for equidistance. Sufficient.

Statement (2) would allow the first case that we thought of, the point at (1, 4), but it doesn't tell us the x coordinate, so all we have is (x, 4). The point could be equidistant from the other two or it could be quite close to one of the points, for example. Statement (2) therefore does not give us data sufficient to answer the question definitively in the positive or the negative.

The correct answer is (A).