go to previous page   go to home page   go to next page

What is the length of the hypotenuse of a right triangle whose two sides are 6 and 8?


length2   =   62 + 82
length2   =   36 + 64 = 100
length    =   10

Formula for Vector Length

3, 4, 5 Right Triangle

The formula for the length of a 2D vector is the Pythagorean Formula. Say that the vector is represented by   (x, y)T.   Put the vector with its tail at the origin. Now make a triangle by drawing the two sides:

side_1   = (x, 0)T

side_2   = (0, y)T.

The length of side_1 is x, and the length of side_2 is y, so:

length (x, y)T   =   ( x2 + y2 )

In this formula, means the positive square root. We don't (of course) want the length to be negative.


What is the length of the vector represented by   ( 4, 3 )T     ?