3D Coordinate System Concepts

This video tutorial covers plotting points in 3D space using the XYZ coordinate system. It explains the axes and how to represent points with ordered triples. The video demonstrates plotting points and using a box to provide perspective. It also covers calculating the distance and midpoint between two points in 3D, extending the 2D distance formula to include the Z component.

What is the third axis introduced in the 3D coordinate system called?

• Z-axis

• Y-axis

• W-axis

• X-axis

How many octants are there in a 3D coordinate system?

• Four

• Six

• Eight

• Ten

In the demonstration, what is the ordered triple for a point that is three units out on the x-axis, no movement on the y-axis, and one unit up on the z-axis?

• (1, 0, 3)

• (0, 3, 1)

• (3, 0, 1)

• (3, 1, 0)

What is the purpose of sketching a box when plotting points in 3D?

• To confuse the viewer

• To give a better 3D perspective

• To make the plot look artistic

• To hide the points

When plotting the point (2, 3, 5), how many units do you move along the z-axis?

• 2 units

• 0 units

• 5 units

• 3 units

What is the first step in finding the distance between two points in 3D space?

• Add the coordinates

• Multiply the coordinates

• Divide the coordinates

• Subtract the coordinates

Which component is added to the 2D distance formula to extend it to 3D?

• W component

• X component

• Z component

• Y component

What is the first step in finding the midpoint of a segment in 3D space?

• Divide the coordinates

• Multiply the coordinates

• Add the coordinates

• Subtract the coordinates

For the midpoint formula in 3D, what operation is performed after adding the corresponding coordinates?

• Subtract by two

• Multiply by two

• Divide by two

• Add two

What is the midpoint of the segment with endpoints (7, 5, 1) and (-3, -4, 9)?

• (4, 0.5, 5)

• (4, -4.5, 5)

• (2, 0.5, 5)

• (2, -4.5, 5)