Objectives:

2. Objectives: Find the distance between two points using the distance formula and Pythagorean�s Theorem. Find the midpoint of a segment.

3. Distance Between Two Points In the last section we learned that whenever you connect two points you create a segment. We also learned every segment has a distance. The distance between two points, or the distance of a segment, is determined by the number of units between the two points.

4. Distance Formula on a Number Line If a segment is on a number line, we simply find its length by using the Distance Formula which states the distance between two points is the absolute value of the difference of the values of the two points. | A � B | = | B � A | = Distance

7. Distance Formula on a Coordinate Plane Segments may also be drawn on coordinate planes. To find the distance between two points on a coordinate plane with coordinates (x1, y1) and (x2, y2) we can use this formula:

8. Distance Formula on a Coordinate Plane � or we can use the Pythagorean Theorem. The Pythagorean Theorem simply states that the square of the hypotenuse equals the sum of the squares of the two legs. a2 + b2 = c2

10. Example 2:

11. Example 2:

13. Midpoint of a Segment The midpoint of a segment is the point halfway between the endpoints of the segment. If X is the midpoint of AB, then AX = XB. To find the midpoint of a segment on a number line find � of the sum of the coordinates of the two endpoints. a + b 2

15. Midpoint of a Segment If the segment is on a coordinate plane, we must use the midpoint formula for coordinate planes which states given a segment with endpoints (x1, y1) and(x2, y2) the midpoint is� M= ( x1 + x2 , y1 + y2 ) 2 2

18. More About Midpoints You can also find the coordinates of an endpoint of a segment if you know the coordinates of the other endpoint and its midpoint.

27. Assignment: Geometry: Pg. 25 � 26, #13 � 28, 31 � 40, 43 - 44 Pre-AP Geometry:  Pg. 25 � 26, #13 - 45