Worksheet: Locating a Point in Space

In this worksheet, we will practice representing and locating a point in space by using a three-dimensional coordinate system.

Q1:

In the figure shown, the points 𝑂 and 𝐴 have coordinates ( 0 , 0 , 0 ) and ( 7 , 5 , 6 ) , respectively. Determine the coordinates of 𝐵 and 𝐶 .

  • A 𝐵 ( 0 , 0 , 6 ) , 𝐶 ( 0 , 5 , 0 )
  • B 𝐵 ( 0 , 7 , 5 ) , 𝐶 ( 0 , 7 , 6 )
  • C 𝐵 ( 7 , 0 , 5 ) , 𝐶 ( 7 , 5 , 0 )
  • D 𝐵 ( 7 , 5 , 0 ) , 𝐶 ( 7 , 0 , 6 )

Q2:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 3 , 3 , 3 )
  • B 𝐴 ( 3 , 3 , 4 )
  • C 𝐴 ( 0 , 0 , 4 )
  • D 𝐴 ( 3 , 3 , 3 )

Q3:

In which of the following coordinate planes does the point ( 7 , 8 , 0 ) lie?

  • A 𝑦 𝑧
  • B 𝑥 𝑧
  • C 𝑥 𝑦

Q4:

Given that the point ( 7 𝑚 , 1 2 𝑚 , 𝑚 ) lies in the 𝑦 𝑧 -plane, what is this point?

  • A ( 0 , 7 , 7 )
  • B ( 7 , 1 2 , 0 )
  • C ( 0 , 1 2 , 7 )
  • D ( 0 , 5 , 7 )

Q5:

Given that the point ( 𝑥 , 𝑦 , 𝑧 ) lies in the 𝑥 𝑦 -plane, determine its 𝑧 -coordinate.

Q6:

Given that the point ( 𝑥 , 𝑦 , 𝑧 ) lies in the 𝑥 𝑧 -plane, determine its 𝑦 -coordinate.

Q7:

Given that the point ( 𝑥 , 𝑦 , 𝑧 ) lies in the 𝑦 𝑧 -plane, determine its 𝑥 -coordinate.

Q8:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 2 , 3 , 3 )
  • B 𝐴 ( 3 , 2 , 4 )
  • C 𝐴 ( 0 , 0 , 4 )
  • D 𝐴 ( 3 , 2 , 3 )

Q9:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 1 , 2 , 5 )
  • B 𝐴 ( 2 , 1 , 6 )
  • C 𝐴 ( 0 , 0 , 6 )
  • D 𝐴 ( 2 , 1 , 5 )

Q10:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 3 , 2 , 4 )
  • B 𝐴 ( 2 , 3 , 5 )
  • C 𝐴 ( 0 , 0 , 5 )
  • D 𝐴 ( 2 , 3 , 4 )

Q11:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 2 , 3 , 2 )
  • B 𝐴 ( 3 , 2 , 3 )
  • C 𝐴 ( 0 , 0 , 3 )
  • D 𝐴 ( 3 , 2 , 2 )

Q12:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 2 , 2 , 4 )
  • B 𝐴 ( 2 , 2 , 5 )
  • C 𝐴 ( 0 , 0 , 5 )
  • D 𝐴 ( 2 , 2 , 4 )

Q13:

Determine the coordinates of point 𝐴 .

  • A 𝐴 ( 2 , 4 , 4 )
  • B 𝐴 ( 4 , 2 , 5 )
  • C 𝐴 ( 0 , 0 , 5 )
  • D 𝐴 ( 4 , 2 , 4 )

Q14:

Determine the coordinates of point 𝐴 .