Distance between two points in the plane?

The distance between two points on a coordinate plane can be expressed using this equation: sqrt(((x2-x1)^2)+((y2-y1)^2))=d.That is the square root of x2 minus x1 squared plus y2 minus y1 squared. Whereas x1 & x2 is the x-coordinate on the two points.

y1 & y2 is the y-coordinate on the two points.

The two points:

(x,y)

(1,3)

(2,4)

x1 = 1

x2 = 2

y1 = 3

y2 = 4

The equation you need to answer your question looks like this:

sqrt(((2-1)^2)+((4-3)^2))=d.That is the square root of x2 minus x1 squared plus y2 minus y1 squared.

Now you make an subtraction:

sqrt(((2-1)^2)+((4-3)^2)) = d

<=>

sqrt((1)^2 + (1)^2) = d

<=>

sqrt(1^2 + 1^2) = d

<=>

sqrt(1 + 1) = d

sqrt(2) = d

You have to imagine there is a triangle between the two points. Hang on I'll try some text art:

--B(2,4) /-|

---------- /--| 1 (this looks funny because of the way it's drawn)

----------/---|

A(1,3)/__|

----------1

(OK that probably isn't very helpful)

The diagonal line is the line between the two points and the straight line are imaginary lines to show the triangle. You can work out the lengths of the straight lines easily by looking at the picture or by subtracting the larger X co-ordinate from the smaller one, and the same for Y. You can then use Pythagoras to calculate the length of the diagonal.

a^2 = b^2 + c^2 (^2 means squared)

a^2 = 1^2 + 1^2

a^2 = 2

a = root(2)

For any two points A( Ax, Ay) and B( Bx, By ) you can use this formula:

a^2 = (Bx - Ax)^2 + (By-Ay)^2

Hope that clears it up

JP L - This feels like an fundamental, even nevertheless it may't be! what is going to you combine, and why? right here the quantity in question is distance, which dpends on discrete factors, no longer a continuos area! Jerome - the factor of rotation differences. additionally, the quantity of rotation is an AP. it is actual no longer a ray sweeping a circle. How did you get to this end? If Jerome is right, please clarify! If he's no longer, consistent with danger utilising complicated factors as a rotating arrow in a airplane could be helpful. The LHS of the equaion could have words like a1 - a2, a2-a3 and such so as that on addition, each and every intermediate term would be cancelled off and we ought to get a1 - a182. If teh RHS can then be simplified and evaluated, you will get your answer.