Q: If p and Q are two points in the plane. the perpendicular bisector of pq is the set of all points equidistant from p and q?

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The set of all points in the plane equidistant from one point in the plane is named a parabola.

End points: (-2, 4) and (-4, 8) Midpoint: (-3, 6) Slope: -2 Perpendicular slope: 1/2 Perpendicular bisector equation: y -6 = 1/2(x--3) => y = 0.5x+7.5

The plane, which passes through the equator of the earth, perpendicular to its axis of rotation, and equidistant from its poles -- is known as Euuatorial plane

a circle, centered at the given point.

parabola

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A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points

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A line that is the angle bisector.

Bisector of an angle, is defined as the set of all points in a plane that are equidistant from the two sides of a given angle.

angle bisector

The set of all points in a plane that are equidistant from the two sides of a given angle

the middle point * * * * * In 2 dimensions: also any point on line forming the perpendicular bisector of the line segment. In 3 dimensions: the plane formed by the perpendicular bisector being rotated along the axis of the line segment. In higher dimensions: Hyperplanes being rotated along the same axis.

A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.

The set of all points in the plane equidistant from one point in the plane is named a parabola.

Points: (-1, 4) and (3, 8) Midpoint (1, 6) Slope: 1 Perpendicular slope: -1 Perpendicular bisector equation: y-6 = -1(x-1) => y = -x+7

a straight line ..