# 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.

## Variations

Attached File(s):