10.7 Distance in Coordinate Geometry

1
10.7 Distance in Coordinate Geometry

• Geometry CP

2
Investigation

• Paul is located at 130th and Q. Katie is at
  170th and Maple.
• If Paul walks on sidewalks along the streets to
  meet Katie, his shortest route is 9 blocks.
• If Paul were able to fly straight to Katie, how
  would you calculate?

180







170
160
150
140
130
120
110
Fort
Maple
Center
Dodge
Pacific
L Street
Q Street
3
Investigation

• If Paul were able to fly straight to Katie, how
  would you calculate?
• Use Pythagorean Theorem
• Assume each block is approximately 50 meters,
  calculate the distance to the nearest meter

180







170
160
c
150
140
130
120
110
(5 blocks)(50m) 250m
Fort
(4 blocks)(50m) 200m
Maple
Center
Dodge
Pacific
L Street
Q Street
C2 (200m)2 (250m)2
C2 40,000m2 62,500m2
C ? 320m
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Investigation

• A grid of streets is like a coordinate plane
• There are 2 sets of parallel lines, one set
  running perpendicular to the other set.
• Thus every segment in the plan (nonvertical and
  nonhorizontal segments) is the hypothenuse of
  some right triangle.
• You can use the Pythagorean Theorem to find the
  distance between two points on a coordinate plane

5
Investigation

• Use handout
• What if I gave you two points that didnt fit on
  your paper? I.e. A (15,37) B (42,73)
• You can find the vertical distance by subtracting
  the y-coordinates of your two points (since
  distance is not negative, subtract the lesser
  coordinate from the greater)
• The horizontal distance if found by subtracting
  the x-coordinates of the two points.
• The distance between A and B or AB
• AB2 (73-37)2 (42-15)2
• AB2 1296 729 2025
• AB 45

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Distance Formula Conjecture
x2, y2
a
x1, y1
b

• Two find the distance between any two points
  (x1,y1) and (x2,y2)

d ?(y2-y1)2 (x2-x1)2
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Examples

• Find the distance between A (8,15) and B
  (-7,23)
• Distance 17
• Find the distance between A (5,12) and B
  (-3,4)
• Distance 8?2 or 11.3

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Homework

• Page 510
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