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

Materials

Graph paper either bold or raise lined
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)

Procedure

Review 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

Variations

This is a short video on that describes how to use the pythagorean theorem to find the distance between two points on a coordinate grid: http://www.sophia.org/tutorials/using-the-pythagorean-theorem-to-find-distance-on