Two or an ext figures that space equal in street from each other, or same in distance from a provided point, are claimed to it is in equidistant, together in the number below.

You are watching: What does equidistant mean in geometry

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We see points that space equidistant all around us. In the chart below, the rails top top a rail track are equidistant, and also each passenger auto on the Ferris wheel is equidistant native the Ferris wheel"s center.

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The midpoint formula and also the street formula can be provided to discover a allude that is equidistant from two points and also to determine whether 2 or much more figures are equidistant.

Midpoint: If (x1, y1) and also (x2, y2) space the endpoints the a heat segment in a 2D coordinate plane, the midpoint the the heat segment is

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The midpoint, by definition, is equidistant native each finish of the heat segment.

Distance formula: If (x1, y1) and also (x2, y2) room two points in a name: coordinates plane, the distance, d, between the 2 points is

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Example:

Find the midpoint of line segment abdominal given that the coordinates of clues A and also B room (1, -2) and (5, 6) respectively. Verify the midpoint by finding its street from clues A and B.

i. Midpoint:

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ii. Distance in between A and also the midpoint:

d1 =
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iii. Distance in between B and the midpoint:

d2 =
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Both points A and B room from the midpoint i beg your pardon confirms that the midpoint is equidistant come points A and B.


Equidistance in geometry

The ide of equidistance is offered throughout geometry. Below are just a couple of examples.

Parallel lines

Parallel lines space equidistant from every other; any suggest on one line is always equal in street from the other line.

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Parallel planes

Like parallel lines, parallel airplane are additionally equidistant from every other. Any allude on one aircraft is same in street from the various other plane.

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Perpendicular bisectors

Any allude on the perpendicular bisector that a line segment is equidistant indigenous the segment"s endpoints.

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Line m is the perpendicular bisector of line segment PQ, shown above. Point out R, T, S, and also U on line m room all equidistant from P and Q.

Circles

Each allude that lies top top a circle is equidistant from the center of the circle. A radius is a line segment that has actually endpoints top top both the circle"s center and the one itself. All radii (plural for radius) have an same length.

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Triangles

The circumcenter the a triangle is the allude of intersection of the three perpendicular bisectors of the triangle"s sides. The circumcenter is equidistant from each of the triangle"s vertices (plural because that vertex).

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The circumcenter the triangle PQR over is allude C. Allude C is equidistant indigenous vertices P, Q, and R. Because C is equidistant from P, Q, and also R, the is feasible to attract a circle focused at C that intersects every the vertices the the triangle. This one is referred to as the circumcircle that the triangle.

Angle bisectors

Any point on an angle"s bisector is equidistant from its sides.

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Ray BG bisects angle alphabet above. Clues G and also F space equidistant from sides BA and BC. The street from each allude on the edge bisector is the length of the line segment perpendicular to every side, as displayed by the blue heat segments.

Parabolas

A parabola is the collection of all points the is equidistant native a addressed point, called the focus, and a solved line referred to as the directrix.

See more: Find The Measure Of Each Minor Arc Formed By A Regular Hexagon Inscribed In A Circle.

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Points A, B, and C, as well as any allude on the parabola, room all equidistant native the parabola"s focus allude and directrix.