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Learn how to measure lengths in geometry using number lines, coordinates, and segment addition postulate. Practice finding distances and midpoints between points with examples. Understand congruency and the Distance Formula.
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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
To find the distance between two points on a number line, take the larger coordinate minus the smaller coordinate. For the previous problem.
The distance between the two points C and H is the same as the length of , which can be writtenas ____ . (Note: _________________).
Consider this number line.Examples: Find the distances. AB = _______ GH = ________ HI= ________ GI = ________
While we are permitted to say AB = GH, we cannot say because they are not the exact same set of points. Instead we write is congruent to
Two segments are congruent if they have the same length. “Tick” marks are used to indicate congruent segments in a figure.
A *midpoint of a segment is the point that divides the segment into two congruent segments.
Example: On the number line at the top of the page, if I is the midpoint of , what is the coordinate of point J?
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.
Example: B is between A and C, AB= 13, BC = 5x and AC = 8x – 7. Determine x, BC and AC.
The Distance Formula and Midpoint FormulaFor any two pointsAB = the midpoint of AB =
Example: If A(-3, 7) and B(9, -2), find AB and the midpoint of .
