Lesson 1-3 Distance and Midpoint.

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Objective Apply the formula for midpoint.
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Presentation transcript:

Lesson 1-3 Distance and Midpoint

5-Minute Check on Lesson 1-2 Transparency 1-3 5-Minute Check on Lesson 1-2 Find the precision for a measurement of 42 cm. If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find x and MN? Use the figure to find RT. Use the figure to determine whether each pair of segments is congruent. MN, QM MQ, NQ If AB  BC, AB = 3x – 2 and BC = 3x + 3, find x. R S T 2⅝ in 5¾ in M Q N 8 cm 6 cm Standardized Test Practice: A 5 B 4 C 3 D 2 Click the mouse button or press the Space Bar to display the answers.

5-Minute Check on Lesson 1-2 Transparency 1-3 5-Minute Check on Lesson 1-2 Find the precision for a measurement of 42 cm. If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find x and MN? Use the figure to find RT. Use the figure to determine whether each pair of segments is congruent. MN, QM MQ, NQ If AB  BC, AB = 4x – 2 and BC = 3x + 3, find x. 42 ± ½ cm or 41.5 cm to 42.5 cm x = 2, MN = 1 R S T 2⅝ in 5¾ in 8 ⅜ M Q N 8 cm 6 cm 8 = 8, Yes 8 ≠ 6, No Standardized Test Practice: A 5 B 4 C 3 D 2 Click the mouse button or press the Space Bar to display the answers.

Objectives Find the distance between two points Find the midpoint of a (line) segment

Vocabulary Midpoint – the point halfway between the endpoints of a segment Segment Bisector – any segment, line or plane that intersects the segment at its midpoint

Distance and Mid-points Review Concept Formula Examples Mid point Nr line Coord Plane (a + b) 2 (2 + 8) 2 [x2+x1] , [y2+y1] 2 2 7 + 1 , 4 + 2 2 2 Distance D = | a – b | D = | 2 – 8| = 6 D = (x2-x1)2 + (y2-y1)2 D = (7-1)2 + (4-2)2 = 40 = 5 = (4, 3) (1,2) (7,4) Y X ∆x ∆y D a b 1 2 3 4 5 6 7 8 9

Use the number line to find AX. Answer: 8 Example 3-1b

Find the distance between E(–4, 1) and F(3, –1). Method 1 Pythagorean Theorem Use the gridlines to form a triangle so you can use the Pythagorean Theorem. Simplify. Take the square root of each side. Example 3-2a

Method 2 Distance Formula Simplify. Simplify. Answer: The distance from E to F is units. You can use a calculator to find that is approximately 7.28. Example 3-2c

The coordinates of J and K are –12 and 16. The coordinates on a number line of J and K are –12 and 16, respectively. Find the coordinate of the midpoint of . J K -12 16 The coordinates of J and K are –12 and 16. Let M be the midpoint of . Simplify. Answer: 2 Example 3-3a

Find the coordinates of M, the midpoint of Find the coordinates of M, the midpoint of , for G(8, –6) and H(–14, 12). Let G be and H be . y x Answer: (–3, 3) Example 3-3b

Let F be in the Midpoint Formula. Find the coordinates of D if E(–6, 4) is the midpoint of and F has coordinates (–5, –3). Let F be in the Midpoint Formula. Write two equations to find the coordinates of D. Example 3-4a

Answer: The coordinates of D are (–7, 11). Solve each equation. Multiply each side by 2. Add 5 to each side. Multiply each side by 2. Add 3 to each side. Answer: The coordinates of D are (–7, 11). Example 3-4b

Summary & Homework Summary: Homework: Distances can be determined on a number line or a coordinate plane by using the Distance Formula The midpoint of a segment is the point halfway between the segment’s endpoints Homework: pg 25-27; 9, 12-15, 20, 23, 37-38, 57, 63, 65