谷歌课堂
GeoGebraGeoGebra 教室

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.

选择所有适用项
  • A
  • B
  • C
  • D
检查答案 (3)

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.