Let A(3, -1) and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance √2 units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?
A.(2, 1)
B.(3, 1)✓ Correct
C.(2, 2)
D.(1, 3)
Explanation
Midpoint P = (2, 0). Slope of AB = (1-(-1))/(1-3) = -1, so perpendicular bisector has slope 1. Direction unit vector along bisector: (1/√2, 1/√2). Q = P ± √2·(1/√2, 1/√2) = (2, 0) ± (1, 1) = (3, 1) or (1, -1). So (3, 1) is among options.
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