Lines and the Coordinate Plane: The Coordinate Plane

Examples

Example 1: Given A(5, 9) and B(2, 5), we find the distance between A and B or the length of AB as follows:

x1 = 5 and x2 = 2

y1 = 9 and y2 = 5

Then

d equals the square root of the quantity x 1 minus x 2 quantity squared plus y 1 minus y 2 quantity squared, d equals the square root of the quantity 5 minus 2 quantity square plus 9 minus 5 quantity squared, d equals the square root of the quantity 3 squared plus 4 squared, d equals the square root of the quantity 9 plus 16, d equals the square root of 25, d equals 5

Example 2: Find the distance of CD if C (1,-3) and D (-2,-7).

d equals the square root of the quantity 1 minus negative 2 quantity squared plus negative 3 minus negative 7 quantity squared, d equals the square root of the quantity 3 squared plus 4 squared, d equals 5

As you can see, AB = CD, even though they have different endpoints.