The document discusses formulas for finding distance and midpoints between points on a coordinate plane. It provides examples of using the distance formula to calculate distances between points and the Pythagorean theorem to find the length of a hypotenuse. It also demonstrates using the midpoint formula, which takes the average of the x-values and y-values of two points to find the midpoint between them. This is then used along with distance calculations to solve problems involving finding distances or midpoints on a map.

1. Midpoint and Distance Formulas North Carolina Standard Course of Study Competency Goal 2 – The learner will describe geometric figures in the coordinate plane algebraically. Objective 2.01 – Find the lengths and midpoints of segments to solve problems.

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

5. Example 3: The vertices of a right triangle are (0, 0), (0, 8) and (8, 0). What is the length of the hypotenuse? ? 8 8 We are going to use the Pythagorean Theorem here. Remember the Pythagorean Theorem is a 2 + b 2 = c 2 . Also remember that a and b are the legs and c is the hypotenuse. In this case 8 and 8 are the legs so we will use those to fill in for a and b.

6. 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.

7. 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.

8. Click on the objects below to view two shot clips of distance and midpoint Distance