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- 1. Today: Warm-Up Make-Up Tests? Alt.Khan Due Today Review: Radical Equations, Pythagorean Theorem, Distance & Midpoint Formulas Class Work STAR Testing May 19
- 2. Radical Operations Review: 10 10S =
- 3. Last Radical Test Review: = 214.86972 feet; = 215 feet Pythagorean Theorem
- 4. Last Radical Test Review: Radical Equations: s = 60 24 + 8q = 9 + 6q + q2 0 = -15 + 2q + q2 q2 - 2q -15 = 0 (q - 5)(q + 3) = 0 q = 5, q = -3Check to see if one or both are extraneous solutions Both are solutions
- 5. The Distance Formula There are two different types of problems to solve withe the distance formula. A. All four of the coordinates are known. Solve for the distance. B. Three of four coordinates and the distance is known. Solve for the fourth coordinate.
- 6. A. All four of the coordinates are known. Solve for the distance.
- 7. B. Three of four coordinates and the distance is known. Solve for the fourth coordinate. a2 – 6a – 16 = 0 (a – 8) (a + 2) = 0 a = 8, a = -2 Plug in to check
- 8. MIDPOINT • The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments. • Just as there are two different types of problems involving the distance formula, there are two different types of midpoint problems. 1. Both endpoints are given, and the midpoint must be found. 2. One endpoint and the midpoint are given; the other endpoint must be found.
- 9. To find the midpoint of the line along the x axis.. Add the |beginning coordinate| and the |ending coordinate|, then ÷ 2 To find the midpoint of the line along the y axis, find the ‘average’ y value The average y value of the line segment is... The mid-point is at (0,5) What are the x coordinates of the end points of the line segment? The average x value of the line segment is... What are the y coordinates of the end points of the line segment? The mid-point coordinates are.. (1,0) The mid-point coordinates are...
- 10. • If the line segments are vertical or horizontal, you may find the midpoint by simply dividing the length of the segment by 2 and counting that value from either of the endpoints. = The Average
- 11. 6 10 Midpoint If the line segments are diagonally positioned, more thought must be paid to the solution. When you are finding the coordinates of the midpoint of a segment, you are actually finding the the x-coordinates and the y-coordinates.
- 12. Midpoint Formula X + X , Y + Y 2 2
- 13. Example 1:
- 14. X1 + X2 2 = XMID Y1 + Y2 2 = YMID What If We Knew The Midpoint Of A Segment And One Endpoint? How Would We Find The Other Endpoint? Think Of The Formula As: Plug in the given and solve for the unknown Given an endpoint ( 3,5 ), and midpoint ( 6, -2 ), find the other endpoint.
- 15. X1 + X2 2 = XMID Y1 + Y2 2 = YMID Find ( X2 ,Y2 ) 3 + X2 = 6 12 5 + Y2 = -2 -4 (9, -9) 3 + X2 = 2 X2 = 9 5 + Y2 = 2 Y2 = -9 ( X2 ,Y2 ) =
- 16. Example 2: M is the mid-point. The coordinates M (-1,1) and C (1,-3) are given. Find the coordinates of point D. Find ( X2 ,Y2 ) X1 + X2 2 = XMID Y1 + Y2 2 = YMID M C D = (-3,5)
- 17. A variation of the second type of midpoint problem. Find the missing value of h in the points (5,7) and (1,h) if its midpoint lies at (3, -2)

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