Worksheet: Coordinates of a Midpoint and an Endpoint in Three Dimensions

In this worksheet, we will practice finding the coordinates of a midpoint and an end point in three dimensions using a formula.

Q1:

Given that the midpoint of 𝐴 𝐵 lies in the 𝑥 𝑦 -plane, and the coordinates of 𝐴 and 𝐵 are ( 1 2 , 9 , 𝑘 + 3 ) and ( 1 5 , 9 , 3 𝑘 ) , respectively, determine the value of 𝑘 .

  • A 4 3
  • B 3 4
  • C 4 3
  • D 3 4

Q2:

Points 𝐴 , 𝐵 have coordinates ( 8 , 8 , 1 2 ) and ( 8 , 5 , 8 ) , respectively. Determine the coordinates of the midpoint of 𝐴 𝐵 .

  • A ( 0 , 3 , 2 0 )
  • B ( 8 , 8 , 2 )
  • C ( 1 6 , 1 3 , 4 )
  • D 0 , 3 2 , 1 0

Q3:

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of 𝐴 𝐵 𝐶 , given that the coordinates of 𝐴 , 𝐵 , and 𝐶 are ( 1 0 , 8 , 2 ) , ( 8 , 7 , 1 0 ) , and ( 2 , 3 , 1 4 ) , respectively.

Q4:

Given that point ( 0 , 1 7 , 1 0 ) is the midpoint of 𝐴 𝐵 and that 𝐴 ( 1 9 , 7 , 1 4 ) , what are the coordinates of 𝐵 ?

  • A ( 1 9 , 4 1 , 6 )
  • B ( 1 9 , 1 0 , 2 4 )
  • C ( 1 9 , 2 4 , 4 )
  • D ( 1 9 , 2 7 , 3 4 )

Q5:

Given that point ( 9 , 1 7 , 1 1 ) is the midpoint of 𝐴 𝐵 and that 𝐴 ( 4 , 2 , 9 ) , what are the coordinates of 𝐵 ?

  • A ( 1 4 , 3 2 , 3 1 )
  • B ( 1 3 , 1 9 , 2 )
  • C ( 5 , 1 5 , 2 0 )
  • D ( 2 2 , 3 6 , 1 3 )

Q6:

Given that point ( 1 , 4 , 1 8 ) is the midpoint of 𝐴 𝐵 and that 𝐴 ( 1 2 , 8 , 1 ) , what are the coordinates of 𝐵 ?

  • A ( 1 0 , 1 6 , 3 7 )
  • B ( 1 3 , 4 , 1 7 )
  • C ( 1 1 , 1 2 , 1 9 )
  • D ( 1 4 , 0 , 3 5 )

Q7:

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of 𝐴 𝐵 𝐶 , given that the coordinates of 𝐴 , 𝐵 , and 𝐶 are ( 1 9 , 1 8 , 4 ) , ( 1 , 4 , 1 6 ) , and ( 1 3 , 1 8 , 3 ) , respectively.

Q8:

Given that the midpoint of 𝐴 𝐵 lies in the 𝑥 𝑧 -plane, and the coordinates of 𝐴 and 𝐵 are ( 1 4 , 𝑘 + 4 , 1 9 ) and ( 1 7 , 2 𝑘 , 1 8 ) , respectively, determine the value of 𝑘 .

  • A 3 4
  • B 4 3
  • C 3 4
  • D 4 3

Q9:

Given that the midpoint of 𝐴 𝐵 lies in the 𝑥 𝑦 -plane, and the coordinates of 𝐴 and 𝐵 are ( 3 , 1 8 , 𝑘 + 5 ) and ( 1 9 , 1 , 5 𝑘 ) , respectively, determine the value of 𝑘 .

  • A 6 5
  • B 5 6
  • C 6 5
  • D 5 6

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