The Distance Formula

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The Distance Formula
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Creating the distance formula

• The distance formula uses the Pythagorean
  Theorem.
• You have two points on a grid with a line drawn
  between them.
• A right triangle is formed from that segment.
• Pythagorean Theorem is applied.

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The Formula

• People greater than us have developed a formula
  that is easier to use.
• If you have two points (x1, y1) and (x2,y2). The
  distance between them is found by

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Example 1

• Find the distance between (1, 3) and (5, -2).
• Plug it into the formula

d 6.4 (to the tenths place)
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Example 2

• Two news helicopters are on their way to a
  political rally, flying at the same altitude.
  One helicopter is 20 mi due west of the rally.
  The other is 15 mi south and 15 mi east of the
  rally. How far apart are the helicopters?
• Write the ordered pairs (pretend the rally is at
  (0, 0)).

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Example 2

• (-20, 0) and (15, -15)
• Plug it into the formula and simplify.

38.1 miles
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Try these

• Find the length of the line segment that connect
  each pair of endpoints.
• (5, 3) (3, 4)
• (7, 2) (1, -2)

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Try these (cont)

• Forest ranges use lookout towers to locate forest
  fires. One tower is 5 km west and 3 km north of
  the fire. A second tower is 3 km west and 4 km
  south of the fire. How far apart are the two
  towers?
• You live three blocks west and four blocks north
  of the library. Your friend lives two blocks
  east and eight blocks north of the library. How
  many blocks apart do you and your friend live?