1 3 Locating Points and Midpoints LESSON 1

1– 3 Locating Points and Midpoints LESSON 1– 3 Locating Points and Midpoints

1– 3 Locating Points and Midpoints Five-Minute Check (over Lesson 1– 2) TEKS Then/Now New Vocabulary Key Concept: Midpoint Formula (on Number Line) Example 1: Real-World Example: Find Midpoint on Number Line Key Concept: Midpoint Formula (in Coordinate Plane) Example 2: Find Midpoint in Coordinate Plane Example 3: Finding Missing Coordinates Example 4: Find Missing Measures Example 5: Locating a Point at Fractional Distances Example 6: Fractional Distances on a Coordinate Plane Example 7: Locating a Point Given a Ratio

1– 3 Locating Points and Midpoints Over Lesson 1– 2 What is the value of x and AB if B is between A and C, AB = 3 x + 2, BC = 7, and AC = 8 x – 1? A. x = 2, AB = 8 B. x = 1, AB = 5 C. D. x = – 2, AB = – 4

1– 3 Locating Points and Midpoints Over Lesson 1– 2 If M is between L and N, LN = 3 x – 1, LM = 4, and MN = x – 1, what is the value of x and MN? A. x = 1, MN = 0 B. x = 2, MN = 1 C. x = 3, MN = 2 D. x = 4, MN = 3

1– 3 Locating Points and Midpoints Over Lesson 1– 2 Find RT. A. . B. in. C. . D. in.

1– 3 Locating Points and Midpoints Over Lesson 1– 2 What segment is congruent to MN? A. MQ B. QN C. NQ D. no congruent segments

1– 3 Locating Points and Midpoints Over Lesson 1– 2 What segment is congruent to NQ? A. MN B. NM C. QM D. no congruent segments

1– 3 Locating Points and Midpoints Over Lesson 1– 2 A. 5 B. 6 C. 14 D. 18

1– 3 Locating Points and Midpoints Targeted TEKS G. 2(A) Determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint. G. 2(B) Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines. Also addresses G. 5(B). Mathematical Processes G. 1(A), G. 1(G)

1– 3 Locating Points and Midpoints You found the distance between two points on a line segment. • Find the midpoint of a segment. • Locate a point on a segment given a fractional distance from one endpoint.

1– 3 Locating Points and Midpoints • midpoint • segment bisector

1– 3 Locating Points and Midpoints

1– 3 Locating Points and Midpoints Find Midpoint on a Number Line DECORATING Marco places a couch so that its end is perpendicular and 2. 5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet? First we must convert 90 inches to 7. 5 feet. The coordinates of the endpoints of the couch are 2. 5 and 10. Let M be the midpoint of the couch. Midpoint Formula x 1 = 2. 5, x 2 = 10

1– 3 Locating Points and Midpoints Find Midpoint on a Number Line Simplify. Answer: The midpoint of the couch back is 6. 25 feet from the wall.

1– 3 Locating Points and Midpoints DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line is the midpoint of the racing strip? A. 330 ft B. 660 ft C. 990 ft D. 1320 ft

1– 3 Locating Points and Midpoints

1– 3 Locating Points and Midpoints

1– 3 Locating Points and Midpoints Find Midpoint in Coordinate Plane Answer: (– 3, 3)

1– 3 Locating Points and Midpoints A. (– 10, – 6) B. (– 5, – 3) C. (6, 12) D. (– 6, – 12)

1– 3 Locating Points and Midpoints Find Missing Coordinates Let D be (x 1, y 1) and F be (x 2, y 2) in the Midpoint Formula. (x 2, y 2) = (– 5, – 3) Write two equations to find the coordinates of D.

1– 3 Locating Points and Midpoints Find Missing Coordinates Midpoint Formula Answer: The coordinates of D are (– 7, 11).

1– 3 Locating Points and Midpoints Find the coordinates of R if N (8, – 3) is the midpoint of RS and S has coordinates (– 1, 5). A. (3. 5, 1) B. (– 10, 13) C. (15, – 1) D. (17, – 11)

1– 3 Locating Points and Midpoints Use Algebra to Find Measures You know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR.

1– 3 Locating Points and Midpoints Use Algebra to Find Measures Because Q is the midpoint, you know that Use this equation and the algebraic measures to find a value for x. Subtract 1 from each side.

1– 3 Locating Points and Midpoints Use Algebra to Find Measures Original measure

1– 3 Locating Points and Midpoints Use Algebra to Find Measures QR = 6 – 3 x Original Measure

1– 3 Locating Points and Midpoints Use Algebra to Find Measures Multiply. Simplify.

1– 3 Locating Points and Midpoints A. 1 B. 10 C. 5 D. 3

1– 3 Locating Points and Midpoints Locating a Point at Fractional Distances BD = |x 2 – x 1| Distance Formula = |-2 - -6| x 1 = -6, x 2 = -2 = |4| or 4 Subtract. The distance between B and D is 4.

1– 3 Locating Points and Midpoints Locating a Point at Fractional Distances Answer: -5

1– 3 Locating Points and Midpoints A. -7 B. 0 C. 2 D. -1

1– 3 Locating Points and Midpoints Fractional Distances on a Coordinate Plane

1– 3 Locating Points and Midpoints

1– 3 Locating Points and Midpoints Answer: P (– 1. 3, -1)

1– 3 Locating Points and Midpoints A. (2, 1. 8) B. (-2, -1. 8) C. (-1. 8, -2) D. (1. 8, 2)

1– 3 Locating Points and Midpoints Locating a Point Given a Ratio

1– 3 Locating Points and Midpoints Locating a Point Given a Ratio Answer: F (– 2, 4. 4)

1– 3 Locating Points and Midpoints A. (3, -0. 4) B. (3, 0. 4) C. (-0. 4, 8. 9) D. (-0. 4, 3. 1)

1– 3 Locating Points and Midpoints LESSON 1– 3 Locating Points and Midpoints