3D Coordinates

​Introduction to 3D Coordinates

Functions with multivariable components (3+ Variables)​

Finland​

​3D Coordinate Systems

3-Dimensional Graphs are commonly called Solid Analytic Geometry. This is created by taking your normal x- and y-axis and adding the z-axis to them, thus creating a 3-dimensional system. 3-Dimensional points are referred to as being in SPACE!

​Distance Formula

One of the key things we need to be able to do is to find the Distance between points, and since these points are 3-Dimensional, we need to Modify our Distance Formula to match...​

​Another Example

​Midpoint Formula

Just like the Distance Formula, we need to re-work our Midpoint Formula to work with 3 Variables. Thankfully, this doesn't create a formula too difficult to work with...​

​Midpoint Example

Multiple Choice

What would be the midpoint between (0, 2, -5) and (3, 4, -2)?

• (3/2, 2, 3/2)

• (3/2, 3, -7/2)

• (-3/2, -3, -3/2)

Multiple Choice

What would be the midpoint between (10, -2, 7) and (4, 6, 15)?

• (11, 2, 7)

• (7, 2, 11)

• (3, 4, 4)

Distance Formula for 3D Coordinates

Same as old Distance Formula, just another parenthesis section with z's under the Square Root

Multiple Choice

What would be the distance between (2, 4, 5) and (1, 10, -6)? [rounded to 3 decimal places]

• -9.876

• 16.547

• 10.453

• 12.570

Multiple Choice

What would be the distance between (0, 11, 3.5) and (-2, -5, 7.4)? [rounded to 3 decimal places]

• 10.112

• 18.956

• 16.589

• 14.324

Multiple Choice

Vector a = 2i + 3j - 5k. What is the value of 3a?

• 3i + 3j - 3k

• 5i + 6j - 8k

• 6i + 9j -15k

• 6i + 6j - 15k

Multiple Choice

#1  Describe the location of point ( -2, 4, -5 ) in relation to the origin.

• Left 2, Up 4, Back 5
• Down 2, Right 4, Back 5
• Back 2, Right 4, Down 5
• Left 2, Right 4, Down 5

Multiple Choice

#8  What are the coordinates of the point shown in the picture.

• ( 2, -4, 3 )
• ( 2, -3, 3 )
• ( 3, -4, 2 )
• (-3, -4, 2 )

Multiple Choice

#7  What are the coordinates of the point shown in the picture.

• ( 0, 1, -1 )
• ( 1, -1, 0 )
• ( 1, 0 -1 )
• ( 1, 1, 1 )

Multiple Choice

Identify the coordinates of the blue dot...

• (2,2,2)

• (1,1,1)

• (1,2,2)

• (2,1,2)