1. Midpoint and Distance Formulas

2. Distance Formula The distance formula is used to find the distance of a line segment.

3. Example 1: Find the distance between the points (-5, -1) and (3, 5)in simplest radical form. distance formula fill in your x- and y-values simplify by subtracting before squaring square each value add your squared values remember the square root of 100 in simplest form is 10

4. Example 2: A coordinate plane is superimposed on a map of North Carolina. Greenville is located at (350, 75) and Charlotte is located at (120, 130). Find the straight-line distance between the two cities. Write your answer in decimal form. answer is 236.48

5. Midpoint Formula The midpoint formula is used to find the middle of a line segment. You take the average of the x-values and take the average of the y-values.

6. Example 4: On a map’s coordinate grid, Greenville is located (-4, 3) and Raleigh is located at (6, 9). The distance from Greenville to Wilson is half the distance from Greenville to Raleigh. What is the approximate distance from Greenville to Wilson? Round your answer to the nearest hundredth. We know that from Greenville to Wilson and from Wilson to Raleigh it is the same distance. So we know that Wilson is our midpoint. Step 1 – Find the midpoint from Greenville to Raleigh (this will give us Wilson’s location on the map. Step 2 – Now that we know the location of Wilson we can use it to find the distance from it to Greenville. Distance is about 5.830951894845… so if we round that to the nearest hundredth it is about 5.83 miles on the map.