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Distance and Midpoint: Lesson 1-3 Transparency

This lesson focuses on finding the distance between two points and the midpoint of a segment. It includes examples and practice problems using the Distance Formula and the Midpoint Formula.

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Distance and Midpoint: Lesson 1-3 Transparency

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  1. Lesson 1-3 Distance and Midpoint

  2. Transparency 1-3 2⅝ in 5¾ in R S T N 8 cm 6 cm M 8 cm Q 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. Standardized Test Practice: A B C D 2 5 4 3 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 1-3 2⅝ in 5¾ in R S T N 8 cm 6 cm M 8 cm Q 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 8 ⅜ 8 = 8, Yes 8 ≠ 6, No Standardized Test Practice: A B C D 2 5 4 3 Click the mouse button or press the Space Bar to display the answers.

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

  5. 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

  6. Distance and Mid-points Review = 5 = (4, 3) Y (7,4) D ∆y a b ∆x (1,2) 1 2 3 4 5 6 7 8 9 X

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

  8. Example 3-2a 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.

  9. 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 Method 2 Distance Formula Distance Formula Simplify.

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

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

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

  13. Example 3-4b 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).

  14. Summary & Homework • Summary: • 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

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