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Lesson: Finding the Coordinates of a Midpoint and an End Point in Three Dimensions

Worksheet • 8 Questions

Q1:

Given that the midpoint of 𝐴 𝐡 lies in the π‘₯ 𝑦 -plane, and the coordinates of 𝐴 and 𝐡 are ( βˆ’ 1 2 , βˆ’ 9 , π‘˜ + 3 ) and ( βˆ’ 1 5 , βˆ’ 9 , 3 π‘˜ ) , respectively, determine the value of π‘˜ .

  • A βˆ’ 3 4
  • B 3 4
  • C βˆ’ 4 3
  • D 4 3

Q2:

Given that the midpoint of 𝐴 𝐡 lies in the π‘₯ 𝑧 -plane, and the coordinates of 𝐴 and 𝐡 are ( βˆ’ 1 4 , π‘˜ + 4 , βˆ’ 1 9 ) and ( 1 7 , 2 π‘˜ , 1 8 ) , respectively, determine the value of π‘˜ .

  • A βˆ’ 4 3
  • B 4 3
  • C βˆ’ 3 4
  • D 3 4

Q3:

Given that the midpoint of 𝐴 𝐡 lies in the π‘₯ 𝑦 -plane, and the coordinates of 𝐴 and 𝐡 are ( 3 , βˆ’ 1 8 , π‘˜ + 5 ) and ( 1 9 , 1 , 5 π‘˜ ) , respectively, determine the value of π‘˜ .

  • A βˆ’ 5 6
  • B 5 6
  • C βˆ’ 6 5
  • D 6 5

Q4:

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of β–³ 𝐴 𝐡 𝐢 , given that the coordinates of 𝐴 , 𝐡 , and 𝐢 are ( βˆ’ 1 0 , βˆ’ 8 , 2 ) , ( βˆ’ 8 , βˆ’ 7 , 1 0 ) , and ( βˆ’ 2 , 3 , βˆ’ 1 4 ) , respectively.

Q5:

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of β–³ 𝐴 𝐡 𝐢 , given that the coordinates of 𝐴 , 𝐡 , and 𝐢 are ( 1 9 , βˆ’ 1 8 , 4 ) , ( 1 , βˆ’ 4 , βˆ’ 1 6 ) , and ( 1 3 , 1 8 , βˆ’ 3 ) , respectively.

Q6:

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

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

Q7:

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

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

Q8:

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

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