Finding the Shortest Distance Between Two Points

By Susan LoFranco on Apr 24, 2017

  • Form right triangles by connecting the origin, a point on the x-axis, and a point on the y-axis (or a point with another point vertical and another point horizontal).

Note: In order to make this lesson more kinesthetic, the teacher makes a right triangle on the floor using masking tape.  There are two parts of the exercise; 1: to have the student prove that the shortest distance between two points is a straight line and 2: to have the student prove that by using the Pythagorean Theorem they will accurately calculate the shortest distance.

  • Understand tracking vertically and horizontally on a coordinate grid


  • Graph paper either bold or raise linedFloor Triangle
  • Dots, Markers
  • Tape to connect dots
  • Straight edge ruler
  • Masking tape to use on the floor  - use a color that offers contrast  or build it up so that it can be felt better by the student 
  • Attached Document -  Floor Triangle (ABC) 






  • Grid worksheetReview Vocabulary: coordinate grid, x-axis, y-axis, coordinates, right angle, hypothenuse, triangle legs, Pythagorean Theorem.
  • Brainstorm with student instances when they might want to find the shortest distance between two points.  (Possible answers include finding a shorter way to a place, discovering who lives closer to a specified location.) 
  • Review with the student the print copy of the Floor Triangle (ABC)  (attached). 
  • The Floor Triangle (ABC)  should already be set up on the floor.  (Teacher Prep)
  • With the student count off the length of each leg of the triangle.
  • Ask the student if there might be a faster way to get from one point on the triangle to another (A to C).
  • Next, again counting, walk off the length of the hypotenuse with the student.
  • Ask the student if this would be an exact answer.  Why, why not and how could you solve for an exact answer?   
  • The student should solve for the length of the hypotenuse using the Pythagorean Theorem
  • Once the student feels comfortable with this have them complete the the Grid Worksheet using the media of their choice. 


distance collage



Distance video screenshot