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# 1-3-Mdpt--Distance.ppt

23 Mar 2023
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### 1-3-Mdpt--Distance.ppt

1. Distance and Midpoint Formula
2. A B The distance from point A to point B is 4 units. Count spaces not lines.
3. E D The distance from point D to point E can be found with a2 + b2 = c2 3 c 4 32 + 42 = c2 5 = c 5
4. You can also use the distance formula. (-3,2) (1,-1) Use ordered pairs. E D
5. The distance between two points (x1,y1) and (x2,y2) is d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2
6. y1 y2 x1 x2 (x1,y1) (x2,y2) lx2-x1l ly2-y1l a2 b2 d c2
7. d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2 a 2 + b2 c = √ Distance formula is based on Pythagorean Theorem.
8. Find distance between (-3,2) and ( 1, -1 ) (x1, y1) (x2, y2) _______________ d = √( 1++3)2 + ( - 1- 2 )2 d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2 1 -3 -1 2
9. Find distance between (-3,2) and ( 1, -1 ) d = √( 1++ 3)2 + ( - 1-2 )2 d = √( 4 )2 + ( - 3 )2 d = √ 16 + 9 d = √25
10. Find distance between (5, 1) and ( 2, -6 ) (x1, y1) (x2, y2) d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2 ( 2 - 5)2 + ( -6 - 1 )2 d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2
11. d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2 d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2 ( 2 - 5)2 + ( -6 - 1 )2 d =√ d =√ d =√ (- 3) 2 + ( - 7 )2 9 + 49 58 = 7.6 careful ! this is not - 32
12. A B The distance from point A to point B is 4 units. The MIDPOINT is 1/2 way.
13. For any 2 points (x1, y1) and (x2, y2) the midpoint is x1 + x2 2 , y1 + y2 2 æ è ç ö ø ÷ (x1,y1) (x2,y2)
14. Find midpoint (7, 2) and ( -3, 6 ) x1 + x2 2 , y1 + y2 2 æ è ç ö ø ÷ (x1, y1) (x2, y2)
15. x1 + x2 2 , y1 + y2 2 æ è ç ö ø ÷ x1 + x2 2 , y1 + y2 2 æ è ç ö ø ÷ -3 + 7 , 6 + 2 2 2 x1 + x2 2 , y1 + y2 2 æ è ç ö ø ÷ 4 , 8 2 2 ( 2, 4) (7, 2) and ( -3, 6 )
16. Segment AB, has one endpoint A (-1,5). The midpoint is C( 7,3). Find the other endpoint B. A C B
17. Endpoint A (-1,5). (x1,y1) Midpoint C( 7,3). Find endpoint B. x1 + x2 2 , y1 + y2 2 æ è ç ö ø ÷ = (7,3) x1 + x2 2 = 7 y1 + y2 2 = 3 -1 5 x2= 15 y2= 1 (15,1)
18. What kind of triangle is this? Find the lengths of the sides. A B C 3 = sides is equilateral. 2 = sides is isosceles. no = sides scalene. d = x2 - x1 ( ) 2 + y2 - y1 ( ) 2
19. The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty.
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