geom. – ch. 1.6a midpoint formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · m is the...
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![Page 1: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/1.jpg)
Geom.–Ch.1.6AMidpointFormula
Mr.Deyo
![Page 2: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/2.jpg)
HomeWork1‐2‐3:1)StormCheckPastedinNotebook?
2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?
![Page 3: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/3.jpg)
Students will apply the midpoint formula to find midpoint and endpoints of a segment.
Students will demonstrate this by completing a graphic organizer and by solving problems in a pair activity.
Learning Target
![Page 4: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/4.jpg)
Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?
![Page 5: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/5.jpg)
1) Midpoint2) Distance3) Hypotenuse4) Leg
Vocabulary
1. Teachersaystheword.• ALLStudentsrepeattheword.
2. Teachercountsoutsyllablesass/hesaystheword.
• ALLstudentsrepeatsyllablecountastheysaytheword.
3. Studentteamscreateaphysicalrepresentationoftheword.
• ClasschoosesonephysicalrepresentationforALLstudents.
4. Studentteamscreateafriendlydefinitionfortheword.
• Classchoosesonefriendlydefinitionfortheword.
![Page 6: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/6.jpg)
DAY 3 and/or DAY 4 1. Review the word
♦ Friendly Definition ♦ Physical Representation
2. Show how the word works ♦ Synonyms/antonym ♦ Word Problems ♦ Related words/phrases ♦ Example/non-example
Friendly Definition Sketch
Wordwork Sentence
DAY 2 1. Review word
♦ Friendly Definition ♦ Physical Representation
2. Draw a sketch
DAY 5 1. Review the word
♦ Friendly definition ♦ Physical Representation
3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
DAY 1 1. Use Visuals
2. Introduce the word ♦ Friendly Definition ♦ Physical Representation
3. Use Cognates
4. Write friendly definition
5. Physical Representation
WordList1. 2. 3. 4.
![Page 7: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/7.jpg)
Notes: A coordinate plane is a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) . The location, or coordinates, of a point are given by an ordered pair (x, y). You can find the midpoint of a segment by using the coordinates of its endpoints. Calculate the average of the x-coordinates and the average of the y-coordinates of the endpoints.
![Page 8: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/8.jpg)
A‐BProblemAnotes:
Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).
![Page 9: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/9.jpg)
A‐BProblemACheck:
Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).
![Page 10: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/10.jpg)
A‐BProblemBSOLVE!!
Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
![Page 11: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/11.jpg)
A‐BProblemBCheck!!
Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
= (–5, 5)
![Page 12: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/12.jpg)
StormCheck(Think,Write,Discuss,Report)
Withoutdoingcalculations,givemetwoexamplesinyourlifewhereyouwanttofindthemidpointofsomething?
Inmyownlife,Itrytofindthemidpointwhen
_______________________________________
andwhen_______________________________
_______________________________________.
![Page 13: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/13.jpg)
A‐BProblemAnotes: Finding the Coordinates of an Endpoint
M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of N. Step 1 Let the coordinates of N equal (x, y). Step 2 Use the Midpoint Formula:
L NM(6, 1)(2, 7) (x, y)
TakeHalfofFormulaandSolveforX TakeHalfofFormula&SolveforY
( , )
![Page 14: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/14.jpg)
A‐BProblemACheck:
Step 3 Find each coordinate separately.
Setthecoordinatesequal.
Multiplybothsidesby2.
12 = 2 + x Simplify.
– 2 –2
10 = x
Subtract.
Simplify.
– 7 –7
The coordinates of N are
–5 = y
2 = 7 + y
L NM(6, 1)(2, 7) (x, y)
(10,-5)
![Page 15: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/15.jpg)
A‐BProblemBSOLVE!!S is the midpoint of RT. R has coordinates (-6,-1) and S has coordinates (-1, 1). Find the coordinates of T. Step 1 Let the coordinates of T equal (x, y). Step 2 Use the Midpoint Formula:
R TS(-1, 1)(-6,-1) (x, y)
TakeHalfofFormulaandSolveforX TakeHalfofFormula&SolveforY
( , )
![Page 16: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/16.jpg)
A‐BProblemBCheck!!Step 3 Find the x-coordinate.
Setthecoordinatesequal.
Multiplybothsidesby2.
–2 = –6 + x Simplify.
+ 6 +6
4 = x
Add.
Simplify.
+ 1 + 1
3 = y
The coordinates of T are
L NM(-1, 1)(-6, -1) (x, y)
(4,3)
2 = –1 + y
![Page 17: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/17.jpg)
StormCheck(Think,Write,Discuss,Report)
Whenyouusethemidpointformulatosolveforamidpointoranendpoint,howdoyouusethesameformuladifferentlyineachcase?
Whensolvingforamidpoint,_______________
_______________________________________
Whensolvingforanendpoint,______________
_______________________________________.
![Page 18: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/18.jpg)
1) Midpoint2) Distance3) Hypotenuse4) Leg
Vocabulary Review
1. Teachersaystheword.• ALLStudentsrepeattheword.
2. Teachercountsoutsyllablesass/hesaystheword.
• ALLstudentsrepeatsyllablecountastheysaytheword.
3. Studentteamscreateaphysicalrepresentationoftheword.
• ClasschoosesonephysicalrepresentationforALLstudents.
4. Studentteamscreateafriendlydefinitionfortheword.
• Classchoosesonefriendlydefinitionfortheword.
![Page 19: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/19.jpg)
Students will apply the midpoint formula to find midpoint and endpoints of a segment.
Students will demonstrate this by completing a graphic organizer and by solving problems in a pair activity.
Learning Target
![Page 20: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/20.jpg)
Ticket OUT.
1. Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).
2. K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of L.
![Page 21: Geom. – Ch. 1.6A Midpoint Formulahelpmeteach.weebly.com/uploads/1/7/1/0/17102056/... · M is the midpoint of LN. L has coordinates (2, 7) and M has coordinates (6, 1). Find the](https://reader034.vdocuments.mx/reader034/viewer/2022042218/5ec3daf3500e2d553a184404/html5/thumbnails/21.jpg)
HomeWork1‐2‐3:1)StormCheckPastedinNotebook?
2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?
TO 2) (17, 13) TO 1) (3, 3)