1 / 17

1-1c: The Coordinate Plane - Distance Formula & Pythagorean Theorem

1-1c: The Coordinate Plane - Distance Formula & Pythagorean Theorem. GSE:. M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. M(G&M)–10–2 Makes and defends conjectures, constructs geometric

moeshe
Download Presentation

1-1c: The Coordinate Plane - Distance Formula & Pythagorean Theorem

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. 1-1c: The Coordinate Plane- Distance Formula & Pythagorean Theorem GSE: M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or across disciplines or contexts (e.g., Pythagorean Theorem

  2. Example:Findthe measure of AB. A B Point A is at 1.5 and B is at 5. So, AB = 5 - 1.5 = 3.5

  3. Example • Find the measure of PR • Ans: |3-(-4)|=|3+4|=7 • Would it matter if I asked for the distance from R to P ?

  4. Ways to find the length of a segment on the coordinate plane • 1) Pythagorean Theorem- Can be used on and off the coordinate plane • 2) Distance Formula – only used on the coordinate plane

  5. 1) Pythagorean Theorem* * Only can be used with Right Triangles What are the parts to a RIGHT Triangle? • Right angle • 2 legs • Hypotenuse Hypotenuse- Side across from the right angle. Always the longest side of a right triangle. LEG Right angle Leg – Sides attached to the Right angle

  6. Pythagorean Formula

  7. Example of Pyth. Th. on the Coordinate Plane Make a right Triangle out of the segment (either way) Find the length of each leg of the right Triangle. Then use the Pythagorean Theorem to find the Original segment JT (the hypotenuse).

  8. Make a Triangle And use the Pythagorean Th. To find the length of AB

  9. Find the length of the segment

  10. Find the length of CD using the Pythagorean Theorem We got 10 by | 6 - - 4| 10 8 We got 8 by | -4 – 4|

  11. Ex. Pythagorean Theorem off the Coordinate Plane • Find the missing segment- Identify the parts of the triangle Leg 5 in Leg2 + Leg2 = Hyp2 Ans: 52 + X2 = 132 Leg 13 in 25 + X 2 = 169 hyp X 2 = 144 X = 12 in

  12. 2) Distance Formula Lets Use the Pythagorean Theorem

  13. d = J (-3,5) T (4,2) x1, y1 x2, y2 Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values (4-(-3))2 + (2-(5))2 (4+3)2 + (2-5)2 (7)2 +(-3)2 58 49+9 ~ = 7.6 ~

  14. Example of the Distance Formula • Find the length of the green segment Ans: 109 or approximately 10.44

  15. Find the distance between A and C

  16. ( ) Congruent Segments • Segments that have the same length.

  17. Assignment

More Related