A Geometry Worksheet - by HelpingWithMath.com

Calculating the Distance Between Two Points

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Follow the steps below (the first one is done for as an example):

  1. Plot the two points with the coordinates shown below.
  2. Draw a line to join them and form a right triangle with this line as the hypotenuse.
  3. Use the coordinates to find the lengths of the short sides of the triangle.
  4. Calculate the distance (d) between the two points (length of the hypotenuse) using the Pythagorean Theorem.

Page 1 of 4: For help and guidance see these examples of how to find the distance between two sets of coordinates.

(3, 2) and (8, 9)

blank x-y coordinate grid

Solution

grid with points (3,2) and (8,9) plotted as part of right triangle

d = √ 52 + 7 2

d = √ 74

d = 8.602

(2,4) and (10,8)

blank x-y coordinate grid

grid with points (2,4) and (10,8) plotted as part of right triangle

d = √ 82 + 4 2

d = √ 80

d = 8.944

 

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Page 2 of 4: For help and guidance see these examples of how to find the distance between two sets of coordinates.

Follow the steps below (the same as Page 1):

  1. Plot the two points with the coordinates shown below.
  2. Draw a line to join them and form a right triangle with this line as the hypotenuse.
  3. Use the coordinates to find the lengths of the short sides of the triangle.
  4. Calculate the distance (d) between the two points (length of the hypotenuse) using the Pythagorean Theorem.

(3, 8) and (7,3)

blank x-y coordinate grid

grid with points (3,8) and (7,3) plotted as part of right triangle

d = √ 42 + 5 2

d = √ 41

d = 6.403

(2,1) and (6,8)

blank x-y coordinate grid

grid with points (2,1) and (6,8) plotted as part of right triangle

d = √ 42 + 7 2

d = √ 65

d = 8.062

 

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Page 3 of 4: For help and guidance see these examples of how to find the distance between two sets of coordinates.

Use the formula below to calculate the distance, (d) between each pair of points.

   
distance = √  (x2 - x1)2 + (y2 - y1)2

 

(3, 2) and (7,5)

Coordinate grid showing points (3, 2) and (7,5) plotted.

 

d = √(7 - 3) 2 + (5 - 2) 2

d = √4 2 + 3 2

d = √16 + 9

d = √25

d = 5

(4,9) and (9,5)

Coordinate grid showing points (4,9) and (9,5)  plotted.

 

d = √(9 - 4) 2 + (5 - 9) 2

d = √5 2 + (-4) 2

d = √25 + 16

d = √41

d = 6.403

(4,8) and (10,4)

Coordinate grid showing points (4,8) and (10,4)  plotted.

 

d = √(10 - 4) 2 + (4 - 8) 2

d = √6 2 + (-4) 2

d = √36 + 16

d = √52

d = 7.211

 

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Page 4 of 4: For help and guidance see these examples of how to find the distance between two sets of coordinates.

Use the formula below to calculate the distance, (d) between each pair of points.

   
distance = √  (x2 - x1)2 + (y2 - y1)2

 

(-3, 2) and (4, 8)

Coordinate grid showing points (-3, 2) and (4, 8) plotted.

 

 

 

d = √(4 - (-3)) 2 + (8 - 2) 2

d = √7 2 + 6 2

d = √49 + 36

d = √85

d = 9.220

 

(-6, -4) and (3, 7)

Coordinate grid showing points (-6, -4) and (3, 7) plotted.

 

d = √(3 - (-6)) 2 + (7 - (-4)) 2

d = √9 2 + 11 2

d = √81 + 121

d = √202

d = 14.213

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Related Resources

The various resources listed below are aligned to the same standard, (8G08) taken from the CCSM (Common Core Standards For Mathematics) as the Geometry Worksheet shown above.

Apply the Pythagorean Theorem to find the distance between two points in a coordinate ...

Page

Worksheets

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Understand and apply the Pythagorean Theorem

 

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