COORDINATE GRAPHS

DISTANCE BETWEEN POINTS

Concept: A coordinate graph is a system for finding the location of a point, or several points, on a flat surface called a plane. A coordinate graph is formed from two axis lines that cross at a point called the origin. The horizontal line is the x-axis and the vertical line is the y-axis. Both lines are marked as number lines with the origin at zero. The axes divide the graph into four quadrants, labeled I, II, III, and IV.

Each point on the grid is named by two numbers, an x-coordinate and a y-coordinate. The x-coordinate is always written first; the y-coordinate is always written second. Together the coordinates are called an ordered pair and are enclosed in parentheses, separated by a comma like this: (x, y) .

You can find the distance between points on a vertical or a horizontal line by counting. For example, on the grid below, point A is 10 units from point B, and point B is 4 units from point C. Note that points ABC form a right triangle.

To find the distance between two points that are not on the same grid line, such as points A and C, use the following steps.

Steps for Finding the Distance Between Points

Step 1 | Assign each point a label, either point 1 or point 2.
Step 2 | Find the coordinates of the two points.
Step 3 | Substitute the X and Y coordinates of Point 1 and Point 2 for the X and Y coordinates in the Distance Between Points Formula below. X1 and Y1 in the formula will now have the same value as the X and Y coordinates in Point 1. X2 and Y2 in the formula will now have the same value as the X and Y coordinates in Point 2. Distance between points =
Step 4 | Solve the Distance Between Points Formula, using the substituted coordinates of the two points.

Example Find the distance between point A and C on the grid above.

Step 1 | Assign each point a label, either point 1 or point 2. | Point A = Point 1 Point C = Point 2
Step 2 | Find the coordinates of the two points. | Point 1 = ( 6 , 5 ) Point 2 = ( 10 , -5 )
Step 3 | Substitute the X and Y coordinates of Point 1 and Point 2 for the X and Y coordinates in the Distance Between Points Formula below. X1 and Y1 in the formula will now have the same value as the X and Y coordinates in Point 1. X2 and Y2 in the formula will now have the same value as the X and Y coordinates in Point 2. Distance between points = |
(x2 – x 1)2 + (y 2 – y 1)2
Will become
(10 – 6)2 + (–5 – 5)2
Step 4 | Solve the Distance Between Points Formula, using the substituted coordinates of the two points. | equals equals equals equals 10.77