Distance on a Plane - MPM 2D€¦ · 2D 2 OLD day 2 Distance on a Plane ANS.notebook 1 September...
Transcript of Distance on a Plane - MPM 2D€¦ · 2D 2 OLD day 2 Distance on a Plane ANS.notebook 1 September...
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2D 2 OLD day 2 Distance on a Plane ANS.notebook
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September 23, 2019
Distance on a Plane
Learning Goals develop formula for finding the distance between 2 points
How do we find the distance between Ottawa and Edmonton on this scaled map using only the coordinates for each city?
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2D 2 OLD day 2 Distance on a Plane ANS.notebook
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September 23, 2019
Measuring a Line
Recall the Pythagorean Theorem
Part A
An accident occurred near Sturgeon Falls. One of the victims needs surgery that is only performed in Toronto and Ottawa. A helicopter will fly the patient to the nearer hospital.
Use the coordinates to determine the distances. (use 1 unit = 100 km)
Accident site (0, 0)Toronto (3, 8)Ottawa (8, 2)
Which hospital should the helicopter go to?
1. Draw an accurate Graph by hand.2. Connect the Accident site and Ottawa.3. Draw a right angled triangle.4. How long is the vertical side? Is it related to the coordinates?5. How long is the horizontal side? Is it related to the coordinates?6. Come up with a formula to use the coordinates to find the length of the line segment.7. Use your formula to find the distance
1. Accident site to Ottawa2. Accident site to Toronto3. Which hospital should the helicopter go to?
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2D 2 OLD day 2 Distance on a Plane ANS.notebook
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September 23, 2019
Part B
Immediately after delivering the accident victim, the helicopter must carry some donated organs to a hospital in Peterborough and to Barrie from there. Help the pilot figure out how long it will take if he is flying with a speed of 150 km/h.
Peterborough (4, 5)Barrie (2, 2)
1. Draw the two new cities on the Graph.2. Connect the Hospital to Peterborough.3. Draw a right angled triangle.4. How long is the vertical side? Is it related to the coordinates?5. How long is the horizontal side? Is it related to the coordinates?6. Come up with a formula to use the coordinates to find the length of the line segment.
How is this formula different from the one is Part A?7. Use your formula to find the distance and time it takes to deliver the organs.
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2D 2 OLD day 2 Distance on a Plane ANS.notebook
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September 23, 2019
Using the Pythagorean Theorem
the Distance Formula on a coordinate plane is
D = √(x2 x1)2 + (y2 y1)
2
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2D 2 OLD day 2 Distance on a Plane ANS.notebook
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September 23, 2019
ex 1) Find the length of the line segment with end points C (8, 4) and D (3, 2).
ex. 2) Find the length of the line segment with end points X (10, 2) and Y (6, 2).
Homework
pg 151 # 8, 12pg 162 # 2ii aceg, 5b, 8, 9
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Attachments
2.2.16 Line Lengths.gsp
SMART Notebook
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