3D Plane Graphing Quiz

The video tutorial explains how to graph a plane in a three-dimensional coordinate system by finding and plotting the X, Y, and Z intercepts. It demonstrates the process using two examples, showing how to form a triangle with the intercepts to represent the plane. The tutorial also discusses using isometric graphing paper and introduces the concept of XY, XZ, and YZ traces for graphing planes.

What is the purpose of using a three-dimensional coordinate system in graphing a plane?

• To represent three variables

• To represent four variables

• To represent two variables

• To represent a single variable

How do you find the x-intercept of a plane?

• Set all variables to zero

• Set y and z to zero and solve for x

• Set x and y to zero and solve for z

• Set x and z to zero and solve for y

What is the x-intercept of the plane x + 3y + 2z = 6?

• (0, 0, 0)

• (0, 0, 6)

• (6, 0, 0)

• (0, 6, 0)

What is the y-intercept of the plane x + 3y + 2z = 6?

• (0, 0, 2)

• (2, 0, 0)

• (0, 0, 0)

• (0, 2, 0)

What is the z-intercept of the plane x + 3y + 2z = 6?

• (0, 0, 3)

• (3, 0, 0)

• (0, 0, 0)

• (0, 3, 0)

How do you sketch a plane using its intercepts?

• By plotting only the x-intercept

• By forming a triangle using the intercepts

• By drawing a circle through the intercepts

• By connecting the intercepts with a straight line

What should you do if an intercept is negative?

• Plot it as a positive intercept

• Extend the axis in the negative direction

• Use a different coordinate system

• Ignore the intercept

In the second example, what is the x-intercept of the plane?

• (0, 0, 4)

• (0, 0, 0)

• (0, 4, 0)

• (4, 0, 0)

In the second example, what is the y-intercept of the plane?

• (0, 8, 0)

• (8, 0, 0)

• (0, 0, 8)

• (0, 0, 0)

What is a trace in the context of graphing a plane?

• A point where the plane meets the origin

• A line where the plane intersects a coordinate plane

• A shadow of the plane on the ground

• A circle around the plane