2Consider this number line Consider this number line. On a number line, the real number assigned to a point is called the _________ of the point. Find the distance between C and H.coordinate
3To find the distance between two points on a number line, take the larger coordinate minus the smaller coordinate.For the previous problem.
4The distance between the two points C and H is the same as the length of , which can be written as ____ . (Note: _________________).
5Consider this number line. Examples: Find the distances. AB = _______ Consider this number line. Examples: Find the distances. AB = _______ GH = ________ HI = ________ GI = ________
6While we are permitted to say AB = GH, we cannot say because they are not the exact same set of points. Instead we writeis congruent to
7Two segments are congruent if they have the same length Two segments are congruent if they have the same length. “Tick” marks are used to indicate congruent segments in a figure.
8A *midpoint of a segment is the point that divides the segment into two congruent segments.
9Example: On the number line at the top of the page, if I is the midpoint of , what is the coordinate of point J?
10On the number line at the top of the page, we determined that On the number line at the top of the page, we determined that This illustrates the next postulate. Postulate 2: Segment Addition Postulate: If R is between P and Q, then ______________ Note: In order for one point to be between two other points, the points must be collinear.
11Example: B is between A and C, AB = 13, BC = 5x and AC = 8x – 7 Example: B is between A and C, AB = 13, BC = 5x and AC = 8x – 7. Determine x, BC and AC.5𝑥+13=8𝑥−7BC= 33 1/3AC= 46 1/320=3𝑥𝑥=20/3
12The Distance Formula and Midpoint Formula For any two points AB = the midpoint of AB =
13Example: If A(-3, 7) and B(9, -2), find AB and the midpoint of .