Pre Algebra Length in the Coordinate Plane

Length in the Coordinate Plane

Find the length of the horizontal line segment with endpoints( - 2,4) and (2,4).

• Find the distance of the x - coordinates.
• 2 - ( - 2) =
• 2 + 2 =

4

Find the length of the vertical line segment with endpoints (5,6) and (5, - 5).

• Find the distance of the y - coordinates.
• 6 - ( - 5) =
• 6 + 5 =

11

Find the length of the hypotenuse of a right triangle with legs of length 3 ft and 8 ft to the nearest foot.

• a² + b² = c²
  a = 3, b = 8
• 3² + 8² = c²
• 9 + 64 = c²
• 73 = c²

c ≈ 9

An archaeologist finds an ancient tool 6 ft south of his home base and a fossil 9 ft east of home base. To the nearest hundredths place, what is the distance between the tool and the fossil?

• Home base:(0,0)
  Ancient tool:(0, - 6)
  Fossil: (9,0)
• a² + b² = c²
  a = distance from home base to tool = 6
  b = distance from home base to fossil = 9
  c = distance between tool and fossil
• 6² + 9² = c²
• 36 + 81 = c²
• c² = 117

c = 10.82 ft

Find the length of the line segment to the nearest hundredth with the given endpoints: A( − 1, − 5), B(1,3).

• a² + b² = c²
  a = difference between the x-coordinates = 1 − ( − 1) = 1 + 1 = 2
  b = difference between the y-coordinates = 3 − ( − 5) = 3 + 8 = 11
  c = length of the line segment
• 2² + 11² = c²
• c² = 4 + 121
• c² = 125

c = 11.18

Find the length of the line segment with the given endpoints: A(8,12), B(8, − 10).

• Points A and B lie on a vertical line, so there is no need to use the Pythagorean Theorem.
• Find the distance between the y-coordinates.
• 12 − ( − 10) =
• 12 + 10 =

22

Your school is 7 mi north of your house. The grocery store is 5 mi west of your house. To the nearest hundredth mile, how far is your school from the grocery store?

• 
• House: (0,0)
  School: (0,7)
  Grocery store: ( − 5,0)
• a² + b² = c²
  a = distance from house to school = 7
  b = distance from house to grocery store = 5
  c = distance from school to grocery store
• 7² + 5² = c²
• 49 + 25 = c²
• c² = 74

c = 8.60 mi

Find the length of the line segment with the given endpoints: A( − 2,5), B(6,5).

• includegraphicsPA-8-2-8.png
• Points A and B lie on a horizontal line, so there is no need to use the Pythagorean Theorem.
• Find the distance between the x-coordinates.
• 6 − ( − 2) =
• 6 + 2 =

8

Louis walks 70 m straight ahead, turns right, and walks 50 m more. How far, to the nearest hundredth meter, is Louis from his starting point?

• 
• Starting point: (0,0)
  First point: (0,70)
  Second point: (50,70)
• a² + b² = c² a = distance from starting point to first point = 70
  b = distance from first point to second point = 50
  c = distance from starting point to second point
• 70² + 50² = c²
• 4,900 + 2,500 = c²
• c² = 7,400

c = 86.02 m

Find the length of the line segment with the given endpoints to the nearest hundredth: J(9,10), K(1, − 2).

• 
• a² + b² = c²
  a = distance between x-coordinates = 9 − 1 = 8
  b = distance between y - coordinates = 10 − ( − 2) = 10 + 2 = 12
  c = length of the line segment
• 8² + 12² = c²
• 64 + 144 = c²
• c² = 208

c = 14.42

Your house is at H(2, − 3), the movie theater is at M(5,4), and the bowling alley is at B( − 4,1). Is the bowling alley or the movie theater closer to your house?

• 
• To solve this problem, use the Pythagorean Theorem twice - once to find the distance from H to M, and again to find the distance from H to B.
• a² + b² = c²
  c = distance from H to M
  a = difference in x-coordinates = 5 − 2 = 3
  b = difference in y-coordinates = 4 − ( − 3) = 4 + 3 = 7
• 3² + 7² = c²
• 9 + 49 = c²
• 58 = c²
• c = 7.62
• x² + y² = z²
  z = distance from H to B
  x = difference in x-coordinates = 2 − ( − 4) = 2 + 4 = 6
  y = difference in y-coordinates = 1 − ( − 3) = 1 + 3 = 4
• 6² + 4² = z²
• 36 + 16 = z²
• z² = 52
• z = 7.21

The bowling alley is closer to your house.

Length in the Coordinate Plane

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

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• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:18
• x-coordinate
• y-coordinate
• Pythagorean Theorem
• Finding Lengths of Line Segments 1:02
• Example: Find the Length of the Horizontal Line Segment
• Finding Lengths of Line Segments 3:50
• Example: Find the Length of the Vertical Line Segment
• Finding Distance in the Coordinate Plane 5:59
• Example: Find the Length of the Hypotenuse
• Extra Example 1: Find the Distance Between Two Points 7:36
• Extra Example 2: Find the Length of the Line Segment 10:13
• Extra Example 3: Find the Length of the Line Segment 14:28
• Extra Example 4: How Far is Your School from the Arcade? 16:02