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

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​Points on a 3D Coordinate

Explore

Fill in the Blanks

Write down the letters with the coordinates: (0,0,0) and (2,0,0)

Example: B(0,0,0) and G(2,0,0)

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.

Fill in the Blanks

Write your workout on your notebook and type your final answer in the format: M(x,y,z)

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

Fill in the Blanks

a) Find the exact distance between points A (–1,2,3) and B (–1,–2,4).

b) Round your answer in (a) to 3 significant figures.

Your Anser should in the form AB = 3.56 (sample answer format)

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

Fill in the Blanks

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 .

a) What will be its coordinates to nearest metre after 30 minutes?

Show your workout on your notebook and then type your final answer in the form: (x,y,z)

Fill in the Blanks

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 .

b) At this time, how far will the drone be from the operator? Give your answer to the nearest metre.

Show your workout on your notebook and then type your final answer in the form: d = 4567 m

Evaluate

On kognity, complete 3.1.1 end of section.

Mr. I'm done!

Now work on your differentiated worksheet.

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