3.1.1 The 3D Coordinate System

3.1.1: The 3-D Co-ordinate System

Lesson Objective:

• Find the midpoint and the distance of any two points in 3D.

​Success Criteria: I can ...

• Understand the formulas for calculating distance and midpoint in 3D space.

• Apply distance and midpoint calculations to solve real-world problems.

• Interpret and analyze geometric relationships using 3D coordinates.

Engage

How can we determine the shortest distance between two points in 3D space?

Engage

How does 3-D co-ordinate Geometry works in real space? Five Practical Examples.

https://www.askiitians.com/blog/co-ordinate-geometry-works-real-space-five-practical-examples/

​Points on a 3D Coordinate

Explore

​Points on a 3D Coordinate

Explore

Match

Match the following Points with their corresponding coordinates

• B

• D

• E

• H

• C

(2,1,0)

(2,0,3)

(0,1,0)

(0,1,3)

(2,1,3)

• (2,1,0)

• (2,0,3)

• (0,1,0)

• (0,1,3)

• (2,1,3)

Explain

​Mid Point of a line segment:
Similar to the midpoint formula in the 2D Cartesian plane, the midpoint of a line segment in 3D is the average of the coordinates of the endpoints.

Match

​ ​ The coordinates of the two of vertices of a parallelogram ABCD are A(2,0,0) and B(0,0,2)

If the intersection of diagonals of the parallelogram is M(0,2,0), find the coordinates of the other vertices.

​ ​ ​

• C

• D

• F

(-2,4,0)

(0,4,-2)

Math is easy!!!!

• (-2,4,0)

• (0,4,-2)

• Math is easy!!!!

Explain

​Distance between 2 points

Elaborate

Consider the following real-world application and answer the questions that follow.

A remote-controlled drone is 500 m north and 200 m east of its operator, and it is 20 m high. It is travelling due north at a constant height at a speed of 2 km h ^–1

Evaluate

On kognity, complete 3.1.1 end of section.

Mr. I'm done!

Now work on your differentiated worksheet.

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