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Distance Between Points

The Distance Formula

The distance d between two points x1,y1 and x2,y2 is given by:

 

d=x2x12+y2y12

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By using the Pythagorean theorem, we can work out the length of the hypotenuse of a right-angled triangle if we know the length of the other two sides. To find the distance between two points x1,y1 and x2,y2, we first locate the points on the Cartesian plane.

 

 

 

Next, we can construct a right triangle by drawing a horizontal line through x1,y1 and a vertical line through x2,y2.

 

 

From the Pythagorean Theorem we know that c=a2+b2.

 

Now, we need to determine the lengths a and b.

 

a=x2x1        b=y2y1

 

Then square each side to get closer to the form  a2+b2.

 

a2= x2x12=x2x12        b2=y2y12=y2y12

 

Then

 

c=a2+b2=x2x12+y2y12 

 

Click or drag two points on the graph, and the distance between them will be computed, along with the two components of the distance.

Check Only use integer coordinates if you want to allow only lattice points to be selected (for example, 2,4 not 1.7,4.4 ).

 

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