1 / 14

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.

moffet
Télécharger la présentation

Distance and Midpoint: Lesson 1-3 Transparency

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related