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What part of the coordinate plane is equidistant from the points A(-3,2) and B(3,2) explain?

source : wyzant.com

What part of the coordinate plane is equidistant from the points A(-3,2) and B(3,2) explain?

Let point A = (3,2) and point B = (-3,2).  Now imagine a point P with coordinates (x,y) in the coordinate plane.  The distance from point A to P is:

dA2 = (y-2)2 + (x-3)2

The distance from from point B to point P is:

dB2 = (y-2)2 + (x-(-3))2 = (y-2)2 + (x+3)2

Point P is equidistant from points A and B if dA = dB (or dA2 = dB2).  So let’s set them equal and solve for x and y:

(y-2)2 + (x-3)2 = (y-2)2 + (x+3)2

(x-3)2 = (x+3)2

x2 – 6x + 9 = x2 + 6x + 9

0 = 12x

x = 0

This is the equation of a vertical line through the point x=0.  In other words, it is the y-axis.  So the part of the plane equidistant from points A and B are all points along the y-axis.

If you plot points A and B on graph, you can see that point B is a reflection of point A across the y-axis.  The y-axis is thus the axis of symmetry and all points along it are equidistant from points A and B.  If you draw a line from point A and point B to any point P on the y-axis, you can see that the distances are equal.

State Plane Coordinates vs. Surface Coordinates - Corps of Discovery

State Plane Coordinates vs. Surface Coordinates – Corps of Discovery – The state plane coordinate system was brought up, and I asked everybody using state plane coordinates to raise their hand. The linear distance between two points on a State coordinate system, as obtained by computation or scaled from the grid, is termed the grid length of the line…Assuming you mean that all points in the plane are equidistant from $A$ and $B$, then notice that the vector $v For calculating a plane you need a point and a normal vector. A point $P$ of your plane is fore sure the center point of $A$ and $B$. (because of the same distances to $A$ and $B$. $The locus of points in a plane that are equidistant from both a point (called the focus) and a line (called the directrix) is, by definition, a parabola. What is the equation of a locus of a moving point which is always equidistant with the x-axis and the point (-7,-8)?

Equation of a plane equidistant from two points $A$ and $B$? – The four parts of a coordinate plane? X-Y Coordinates Origin Quadrants Points The proper answer is a QUADRANT. 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…A plane coordinate system can be thought of as the juxtaposition of any two measurement scales. One disadvantage of the UTM system is that multiple coordinate systems must be used to account for If you were to plot the points representing the two cities on a map, ignoring the fact that the two…Let P (x, y) be the point equidistant from these three points. Let the coordinates be A(5,1), B(3,-7) and C(7,-1) and the required point be P(x,y). since it is equidistant: Distance between : AP=CP=BP.

Equation of a plane equidistant from two points $A$ and $B$?

What is the locus of a point equidistance from (-a, 0) and x=a line? – The Rectangular Coordinate System / Cartesian Plane. Graphing Points & Identifying Quadrants on the Coordinate Plane.When a point moves in a plane according to some given conditions the path along which it moves is Example: Construct the locus of point P moving equidistant from fixed points X and Y and XY = 6 A cat is free to roam all parts of the garden but is not allowed within 3 m of the house by its owner.Q: Given 2 points A & B and a line L. Points and line are 3D. How to find a point on the given line L which is equidistant from the given points A & B? Note that although all these equations seem to be quadtratic, the square of Px we be scratched because it appears on both sides of the equation.

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