What part of the coordinate plane is equidistant from the points A(–3,2) and B(3,2)? Explain your answer.
Points that are equidistant from A and B lie on the perpendicular bisector of the line segment AB.
The line segment AB has endpoints A(-3,2) and B(3,2). The midpoint of AB is found by averaging the x-coordinates and the y-coordinates of A and B.
The x-coordinate of the midpoint is: (-3 + 3)/2 = 0
The y-coordinate of the midpoint is: (2 + 2)/2 = 2
Therefore, the midpoint of AB is (0,2).
The perpendicular bisector of AB is a straight line that passes through the midpoint of AB and is perpendicular to AB.
Since AB is a horizontal line with a y-coordinate of 2, the perpendicular bisector must be a vertical line passing through the midpoint.
Every point on this vertical line has a y-coordinate of 2 and can have any x-coordinate since it is perpendicular to AB.
Therefore, the set of points equidistant from A and B forms a vertical line passing through the point (0,2) in the coordinate plane.