Pythagorean theorem distance between two points calculator

Find the distance between the given pairs of points.

Distance Between two Points calculator calculates the distance between two given points co-ordinates (x1 , y1) and (x2 , y2) in the XY plane by applying the pythagorean theorem.

Distance Formula

d = √ (x2 – x1)2 + (y2 - y1)2

To find the distance between two points (x1,y1) and (x2,y2),
we first get the distance of x and y axis as :
x = (x2 - x1) and y = (y2 - y1).
now we apply the formula of Pythagorean theorem. $$ distance = \sqrt{ x^{2} + y^{2}} $$ Let's take the example as given coordinates for two points as:
one point is (1 , 3) and second point is (8 , 6)
we will find the distance of x and y axis as follows:
$$x = (8 - 1) = 7$$ $$y = (6 - 3) = 3$$ $$ distace = \sqrt {(7)^{2} + (3)^{2}} $$ $$ = \sqrt {49 + 9}$$ $$ = \sqrt {58}$$

If you want to calculate distance between two points of cartesian coordinates, you can use the below 2D distance calculators. You have to enter the two points which is denoted by (x1, y1) and (x2, y2). </p><div class="form-entry p-5 mb-5"><div class="container"><h2 class="text-center">Distance between Two Points Calculator</h2><p class="text-center">Fill the coordinate &amp; click on calculate button to calculate </p><hr class="my-3 mx-5 hrline"><form method="POST" id="form"><input type="hidden" name="csrfmiddlewaretoken" value="fcchVZYG6jk1g7QoTbmRcuHQ9gJhmJYIhbreOyrlngLCDAzgPVTi2Kdtjea0y2mG"><div class="form-row"><div class="form-group col-md-4"><p class="font-weight-bold">First Co-Ordinate </p></div><div class="form-group col-md-4"><div class="input-group mb-3"><div class="input-group-prepend"><span class="input-group-text" id="basic-addon1">X₁</span></div><input type="number" step="any" required class="form-control" id="x1" placeholder="X1"></div></div><div class="form-group col-md-4"><div class="input-group mb-3"><div class="input-group-prepend"><span class="input-group-text" id="basic-addon1">Y₁</span></div><input type="number" step="any" required class="form-control" id="y1" placeholder="Y1"></div></div></div><div class="form-row"><div class="form-group col-md-4"><p class="font-weight-bold">Second Co-Ordinate </p></div><div class="form-group col-md-4"><div class="input-group mb-3"><div class="input-group-prepend"><span class="input-group-text" id="basic-addon1">X₂</span></div><input type="number" step="any" required class="form-control" id="x2" placeholder="X2"></div></div><div class="form-group col-md-4"><div class="input-group mb-3"><div class="input-group-prepend"><span class="input-group-text" id="basic-addon1">Y₂</span></div><input type="number" step="any" required class="form-control" id="y2" placeholder="Y2"></div></div></div><button type="submit" class="btn btn-block btn-dark">Calculate</button></form></div></div><table class="table table-striped" id="scrollResults"><thead><tr><th scope="col" class="bg-success text-light text-center h4" colspan="3">Distance between Two Points Calculator</th></tr></thead><tbody><tr><th scope="row">First Co-Ordinate</th><th scope="row">( X₁, Y₁) </th><td class="text-success font-weight-bold" id="numberOneInput">(<span id="x1input">0</span>,<span id="y1input">0</span>) </td></tr><tr><th scope="row">Second Co-Ordinate</th><th scope="row">( X₂, Y₂)</th><td class="text-success font-weight-bold">(<span id="x2input">0</span>,<span id="y2input">0</span>) </td></tr><tr><th scope="row">Distance between Two Points </th><th scope="row">√(( X₁- X₂) ²+( Y₁- Y₂) ²)</th><td class="text-success font-weight-bold" id="results"> O Units </td></tr></tbody></table><div class="border-top-0 p-1 mydescriptions"><span id="ezoic-pub-ad-placeholder-112" class="ezoic-adpicker-ad"></span><span class="ezoic-ad ezoic-at-0 medrectangle-3 medrectangle-3112 adtester-container adtester-container-112" data-ez-name="calculatorpack_com-medrectangle-3"><span id="div-gpt-ad-calculatorpack_com-medrectangle-3-0" ezaw="468" ezah="60" style="position:relative;z-index:0;display:inline-block;padding:0;min-height:60px;min-width:468px" class="ezoic-ad"><script data-ezscrex="false" data-cfasync="false" type="text/javascript" style="display:none">if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[468,60],'calculatorpack_com-medrectangle-3','ezslot_7',112,'0','0'])};__ez_fad_position('div-gpt-ad-calculatorpack_com-medrectangle-3-0');

What is Rectangular Cartesian Coordinate?

For determining the proper position of any definite point, it is necessary to know the distance of the definite point from the straight-line bisectors constructed on the plane. It is said as a reason that only a point can lie at any definite distance from two straight line bisectors.

If two such straight lines XOX and YOY are drawn that intersect each other at a right angle on any plane, XOX is called the x-axis, YOY' is called the y-axis and the intersecting point O is called the origin.

Now, let P  be any point on the plane of the two axes. from point P, on XOX’ i.e., the x-axis and on YOY' i.e., the y-axis, the perpendiculars are respectively PM and PN.

Then the distance of point P from the y-axis = NP = 0M = x is called the abscissa of P or x-coordinate.  Again, the distance of P from the x-axis == MP = ON = y is called the ordinate of p or y-coordinate. The abscissa and the Ordinate are jointly called the Coordinate.

 So, in the figure, the coordinate of P means the perpendicular distance of P from the y-axis and the x-axis and by denoting them as x and y, the coordinate of P is expressed by the symbol P(x,y)

The coordinate index (x, y) means an ordered pair whose first element indicates the abscissa and the second element indicates the ordinate. so, if y, by (x, y) and (y, T), two different points are meant.

Therefore, the coordinate of any point depending on two axes intersecting each other at the right angle is called the Rectangular Cartesian Coordinates. If the point is placed at the right side of the y-axis, the abscissa will be positive and if it is placed at the left side, the abscissa will be negative. Again, if the point is placed above the X-axis, the ordinate will be positive and if it is placed below, the ordinate will be negative. On the x-axis, the ordinate will be zero and on y-axis, the abscissa will be zero.

So, the positive abscissa and the ordinate of any point will be along OX and OY respectively or parallel to them. Similarly, the negative abscissa or the ordinate will be along OX' and OY' respectively or parallel to them.

By the two axes Of the Cartesian coordinates, the plane is divided into XOY, YOX' X'OY', Y'OX these four parts. Each of them is called a quadrant. The quadrant XOY is taken as the first and by turns the second, the third and the fourth quadrant remain in anti-clockwise order. According to the sign of the point of the coordinate, the point lies on the different quadrants.

How to Calculate Distance between two points?

Let, P (x1, y1) and Q (x1, y1) be the two different points on a plane. from points P and Q, perpendiculars PM and QN are drawn on x-axis. Again, from point P, draw perpendicular PR on QN.

Now the abscissa of point P is = 0M = x1 and the ordinate of point P is = MP = y1.

The abscissa of point Q is = ON = x2 and the ordinate NQ is = y2.

From the figure we get,

PR = MN = ON-OM = x2 - x1

QR = NQ -NR = NQ-MP = y2-y1

As per the construction, PQR is a right-angled triangle and PQ is the hypotenuse of the triangle. So, as per the theorem of Pythagoras,

PQ² = PR² + QR²

or, PQ = √(PR² + QR² )

Therefore the distance between two Cartesian points is: √(PR² + QR² )

Example: Find the distance between 1,1 and (2,2)

Solution:

Let P (1,1) and Q (2,2) be the given two points/ The distance between two points is

PQ = √((2-1)² + (2-1)² )

PQ = √(1²+ 1² )

PQ = √1+1

PQ = 1.4142

How do you calculate the distance between two points in space?

The distance between two points in space can be calculated using the Pythagorean theorem. This theorem states that in a right angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if you know the lengths of two sides of a triangle, you can calculate the length of the third side using the following formula:

Hypotenuse²  = Side1²  + Side2²

For example, if you wanted to calculate the distance between two points that were 3 units apart horizontally and 4 units apart vertically, you would use the following formula:

Distance = 3² + 4² = 9 + 16 = 25 = 5 units

How do you find the distance between two points on a coordinate plane?

There are a few different ways that you can find the distance between two points on a coordinate plane. One way is to use the Pythagorean theorem. This theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, if you have a triangle with sides of length a, b, and c, and c is the hypotenuse, then the following equation will always hold true: a^2 + b^2 = c^2. This theorem can be used to find the distance between two points on a coordinate plane by treating the line segment connecting the two points as the hypotenuse of a right angled triangle. The length of the other two sides of the triangle can be found by looking at the coordinates of the points - the length of one side will be the difference in the x-coordinates of the two points, and the length of the other side will be the difference in the y-coordinates of the two points. Once you have the lengths of all three sides of the triangle, you can use the Pythagorean theorem to find the length of the hypotenuse, which is the distance between the two points.

What is the distance between two points?

The distance between two points is the length of the straight line that connects them.

How do you find the distance between two points on a graph?

There are a few different ways to find the distance between two points on a graph. One way is to use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. This theorem can be used to find the distance between two points if the coordinates of the points are known. Another way to find the distance between two points is to use the distance formula, which is derived from the Pythagorean theorem. The distance formula is d = √((x_2-x_1)^2+(y_2-y_1)^2), where d is the distance between the points, x_1 and x_2 are the x-coordinates of the points, and y_1 and y_2 are the y-coordinates of the points.

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