Length of a Two-Dimensional Line – Example – 2

To find the length of a Two-Dimensional Line, let’s take the following line, AB.

2D Example - 2.png

We can use the equation for the length of a Two-Dimensional Line, to find the length of AB.

2d Length Equation - 4

In this case, x1 is 9, x2 is -1, y1 is 2, and y2 is 6. Plugging those values into the equation gives us:

2D Example - 2 - 1.png

 

Subtracting the-9 from the -1 gives us 10, and subtracting 2 from 6 gives us -4.

2D Example - 2 - 2.png

 

Squaring the 10 gives us 100, and squaring the 4 gives us 16.

2D Example - 2 - 3.png

 

Adding the 16 and 100 together gives us 116, so the length of the line is the square root of 116.

2D Example - 2 - 4.png

While 116 is not a perfect square, it is a multiple of 4, which is a perfect square so we can factor out a 4 to simplify the radical. So, the square root of 116 can simplify down to 2 times the square root of 29.

2D Example - 2 - 5.png