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-- Draw a line segment from one point to the other.

-- Construct the perpendicular bisector of the line segment..

-- Every point on the perpendicular bisector of the line segment

is equidistant from the two original points.

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Whereupon the first contributor observed:

Yes, that works, no matter how you set the compass, as long as it's more than 1/2 the distance

between the two points. Every setting of the compass will give you a pair of points that are

equal distances from the original two. As you find more and more of them ... with different

settings of the compass ... you'll see that all the equal-distance points you're finding all lie

on the same straight line. That line is the perpendicular bisector of the line between the two

original points, just as we described up above.

Q: How do you find a point which is equidistant from two other points?

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The equidistant point of a straight line is the middle. Measure the distance from one end to the other and half it.

Bisect two arcs above and below the given points or line and the perpendicular of these arcs cuts through the midpoint.

It is the circumcentre of the triangle formed by the three points. Draw the perpendicular bisectors of two of the lines joining the three points. They will meet at the point that is equidistant from the three points.

For three points, (x1,y1), (x2,y2) & (x3,y3), you can set up 3 distance equations with variables x, y & z: z^2 = (x-x1)^2 + (y-y1)^2 z^2 = (x-x2)^2 + (y-y2)^2 z^2 = (x-x3)^2 + (y-y3)^2 3 equations and 3 variables....Solve away! z is your distance. x & y are the coordinates of the equidistant point.

You can't. There are an infinite number of lines that pass through the point (-2, 3).They all have different y-intercepts and different slopes.In order to narrow it down to a single line, you have to give more information.One more point would do it.=======================================================Here's the minimum information needed to define a unique line:-- you name 2 points; I find slope, intercept, and all other points.-- you name one point and one intercept ... 'x' or 'y'; I find slope and all other points.-- you name x-intercept and y-intercept; I find slope and all other points.-- you name one point and the slope; I find intercept and all other points.-- you name one intercept and the slope; I find all other points.

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To find a point equidistant from three other points, construct perpendicular bisectors for two of the segments formed from three points. Note: this will be the center of the circle that has all three points on it's circumference. Three points, not in a straight line, form three pairs of points with each pair defining a different line. Take any pair of points and draw the perpendicular bisector of the line joining them. Repeat for one of the other pairs. These two perpendicular bisectors will meet at the point which is equidistant from all three points - the circumcenter of the triangle formed by the three points.

The equidistant point of a straight line is the middle. Measure the distance from one end to the other and half it.

In spherical geometry we look at the globe as the sphere S^2. Any plane intersecting the sphere will create a great circle. Now if you take any point on the globe and reflect it across that plane, you have another point that is equidistant from the plane. The sets of all these points will be equidistant from the great circle.

Bisect two arcs above and below the given points or line and the perpendicular of these arcs cuts through the midpoint.

It is the circumcentre of the triangle formed by the three points. Draw the perpendicular bisectors of two of the lines joining the three points. They will meet at the point that is equidistant from the three points.

For three points, (x1,y1), (x2,y2) & (x3,y3), you can set up 3 distance equations with variables x, y & z: z^2 = (x-x1)^2 + (y-y1)^2 z^2 = (x-x2)^2 + (y-y2)^2 z^2 = (x-x3)^2 + (y-y3)^2 3 equations and 3 variables....Solve away! z is your distance. x & y are the coordinates of the equidistant point.

since you know of one points and the halfway point between the other point. just multiply the halfway point by 2 and this is the total distance between the two points.

You can't. There are an infinite number of lines that pass through the point (-2, 3).They all have different y-intercepts and different slopes.In order to narrow it down to a single line, you have to give more information.One more point would do it.=======================================================Here's the minimum information needed to define a unique line:-- you name 2 points; I find slope, intercept, and all other points.-- you name one point and one intercept ... 'x' or 'y'; I find slope and all other points.-- you name x-intercept and y-intercept; I find slope and all other points.-- you name one point and the slope; I find intercept and all other points.-- you name one intercept and the slope; I find all other points.

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.

It takes 3 non collinear points to define one specific circle. With only two points an infinite number of circles can be drawn. Proof: Given two points A, B draw the line between them. Then find the perpendicular bisector of the line AB. Any point on the perpendicular bisector is equidistant from the two original points, A and B. A circle with center C and radius AC will then pass through points A and B. There are infinite point C's on the perpendicular bisector so there are infinite circles. Given three points A, B and D you can find the perpendicular bisector for line segements AB and then the perpendicular bisector fof line segment BC. The two perpedicular bisectors will not be parallel because the points A, B and D are non collinear. This means the two perpeniducar bisectors will intercept at only one point C(like any two intercepting lines). This point C is equidistant from points A, B, and D. A circle with center C and radius AC will then pass through all three of the points. Since there is only one point C that lies on both perpendicular bisectors, there is only one circle possible.

Assuming the question should have said x = 3 and x = 7, the answer is x= 5.

A form of arch defined by a moving point which remains equidistant from a fixed point inside the arch and a moving point along a line. This shape when inverted into an arch structure results in a form which allows equal vertical loading along its length. A parabola is the graph of a quadratic equation. Mathworld has some nice drawings. Need a link? You got it. A Parabola is the set of all points that are equidistant from a point and a line. The line is called the directrix and the point is called the focus. Each point on the parabola is as far from the directrix as it is from the focus. It is the same shape of a curve you will find in the reflector of a flashlight bulb, or in the arc of a baseball when it is thrown or hit.