Distance Between Two Points

Learning Goal

Students will explore distance between two points in a coordinate plane and learn how this relates to right triangles.

Visual 1: Click, drag, and drop the points to explore the distance between them.

Question 1: Use the visual to...

Find the distance between each set of two points:

  1. (0,0) and (5,0)
  2. (0,0) and (0,5)
  3. (7,3) and (5,3)
  4. (-6,-4) and (-6,4)
Explain how you know.

Question 1: Check your answer.

Visual 2: Click, drag, and drop the points to explore the distance between them.

Question 2: Use the visual to...

Find the distance between (1,1) and (8,6).

  1. What is different this time?
  2. Can this exact distance be found? Why or why not?

Question 2: Check your answer.

Attention: Did you notice the right triangle?

Attention: Did you notice the right triangle?

Wherever there is a diagonal distance, there is also a right triangle.

  • The longest side of the right triangle (called the hypotenuse) is the diagonal distance.
  • The two shorter sides of the right triangle (called the legs) make up the horizontal and vertical components of the diagonal distance.
Click the most correct choice.

Check all that apply

Visual 3: Click, drag, and drop the points and the lengths to estimate the distance.

Question 3: Use the visual to...

Estimate the distance between each set of two points in terms of the lengths of the hypotenuse and legs of the right triangle:

  1. (0,0) and (6,3)
  2. (-3,5) and (2,1)
  3. (-7,-4) and (3,-8)
  4. (4,-2) and (0,2)
What patterns are there between these lengths? Use the words hypotenuse and leg.

Question 3: Check your answer.