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Can you identify an example of 2 points on the map?

Can you identify an example of 2 points on the map?. Can you identify an example of 2 lines on the map?. Can you identify an example of a plane on the map?. P. point. Names a location NO size Represented by a dot Named with a capital letter. m. line. X Y Z. A straight path

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Can you identify an example of 2 points on the map?

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  1. Can you identify an example of 2 points on the map?

  2. Can you identify an example of 2 lines on the map?

  3. Can you identify an example of a plane on the map?

  4. P point • Names a location • NO size • Represented by a dot • Named with a capital letter

  5. m line X Y Z • A straight path • NO thickness • Extends forever • Use a lower case letter or any two points on the line

  6. R plane A  B C • A flat surface • No thickness • Extends forever • Name with a script capital letter or with three points not on the same line

  7. Segment (line segment) • The part of a line consisting of two points and all the points between them A B

  8. ray • A part of a line that starts at an endpoint and extends forever in one direction R S

  9. Opposite rays • Two rays that share a common endpoint R S T

  10. collinear • Points that lie on the same line

  11. coplaner • Points that lie on the same plane

  12. Important postulates • Through any 2 points there is exactly one line • Through any 3 non-collinear points there is exactly one plane • If 2 points lie in a plane, then the line containing the points lies in the plane

  13. The distance between any two points is the absolute value of the difference of the coordinates. The distance between A and B is also called the length of AB, or AB. A B AB = |a – b| or |b - a| a b

  14. Example 1: Finding the Length of a Segment Find each length. A. BC B. AC BC = |1 – 3| AC = |–2 – 3| = |1 – 3| = |– 5| = 2 = 5

  15. Check It Out! Example 1b Find each length. b. XZ a. XY

  16. In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC.

  17. – 6 –6 Example 2A: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH. FH = FG + GH Seg. Add. Postulate 11= 6 + GH 5 = GH

  18. – 2 – 2 –3x –3x 2 2 Example 2B: Using the Segment Addition Postulate M is between N and O. Find NO. NM + MO = NO Seg. Add. Postulate 17 + (3x – 5) = 5x + 2 3x + 12 = 5x + 2 3x + 10 = 5x 10 = 2x 5 = x

  19. Congruent segments are segments that have the same length. In the diagram, PQ = RS, so you can write PQRS. This is read as “segment PQ is congruent to segment RS.” Tick marks are used in a figure to show congruent segments.

  20. The midpointM of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3. Part 3: MIDPOINTS

  21. Example 3a: Recreation Application The map shows the route for a race. You are at X, 6000 ft from the first checkpoint C. The second checkpoint D is located at the midpoint between C and the end of the race Y. The total race is 3 miles. How far apart are the 2 checkpoints? XY = 3(5280 ft) Convert race distance to feet. = 15,840 ft

  22. – 6000 – 6000 Example 3a Continued XC + CY = XY Seg. Add. Post. 6000 + CY = 15,840 CY = 9840 = 4920 ft The checkpoints are 4920 ft apart.

  23. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. 15 3x = 3 3 –4x –4x +9 + 9 Example 3b: Using Midpoints to Find Lengths E D 4x + 6 F 7x – 9 Step 1 Solve for x. ED = DF 4x + 6 = 7x – 9 6 = 3x – 9 15 = 3x x = 5

  24. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. Example 3b Continued E D 4x + 6 F 7x – 9 Step 2 Find ED, DF, and EF. ED = 4x + 6 DF = 7x – 9 EF = ED + DF = 4(5) + 6 = 7(5) – 9 = 26 + 26 = 52 = 26 = 26

  25. S is the mdpt. of RT. +3x +3x Check It Out! Example 3c S is the midpoint of RT, RS = –2x, and ST = –3x – 2. Find RS, ST, and RT. R S T –2x –3x – 2 Step 1 Solve for x. RS = ST –2x = –3x – 2 x = –2

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