The horizontal and vertical changes between two points form the perpendicular sides of a right triangle. Pythagoras gives AB=sqrt((x_B-x_A)2+(y_B-y_A)2). Distance is nonnegative even when a coordinate change is negative. Example For A(-1,1) and B(3,4), AB=sqrt(42+32)=5 units. Reversing both subtraction orders gives the same distance after squaring. Do not confuse distance with gradient: here the gradient is 34, not 5.

The horizontal and vertical changes between two points form the perpendicular sides of a right triangle. Pythagoras gives \(AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\). Distance is nonnegative even when a coordinate change is negative.

For \(A(-1,1)\) and \(B(3,4)\), \(AB=\sqrt{4^2+3^2}=5\) units.

Reversing both subtraction orders gives the same distance after squaring. Do not confuse distance with gradient: here the gradient is \(\dfrac34\), not \(5\).

Distance between two points

Distance between two points