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Lesson: Converting Points from Polar to Rectangular Coordinates

Worksheet • 11 Questions

Q1:

Given that the polar coordinates of point 𝐴 are ( 4 , 1 2 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€» βˆ’ 2 , 2 √ 3 
  • B ο€» 2 √ 3 , βˆ’ 2 
  • C ο€» βˆ’ 2 , βˆ’ 2 √ 3 
  • D ο€» 2 , βˆ’ 2 √ 3 

Q2:

Given that the polar coordinates of point 𝐴 are ( 3 , 6 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ 3 2 , 3 √ 3 2 
  • B ο€Ώ 3 √ 3 2 , 3 2 
  • C ο€Ώ 3 2 , βˆ’ 3 √ 3 2 
  • D ο€Ώ βˆ’ 3 2 , βˆ’ 3 √ 3 2 

Q3:

Given that the polar coordinates of point 𝐴 are ( 7 , βˆ’ 1 2 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ βˆ’ 7 2 , βˆ’ 7 √ 3 2 
  • B ο€Ώ βˆ’ 7 √ 3 2 , βˆ’ 7 2 
  • C ο€Ώ βˆ’ 7 2 , 7 √ 3 2 
  • D ο€Ώ 7 2 , 7 √ 3 2 

Q4:

Given that the polar coordinates of point 𝐴 are ( 6 , 1 5 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€» βˆ’ 3 √ 3 , 3 
  • B ο€» 3 , βˆ’ 3 √ 3 
  • C ο€» βˆ’ 3 √ 3 , βˆ’ 3 
  • D ο€» 3 √ 3 , βˆ’ 3 

Q5:

Given that the polar coordinates of point 𝐴 are ( 1 , 1 5 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ βˆ’ √ 3 2 , 1 2 
  • B ο€Ώ 1 2 , βˆ’ √ 3 2 
  • C ο€Ώ βˆ’ √ 3 2 , βˆ’ 1 2 
  • D ο€Ώ √ 3 2 , βˆ’ 1 2 

Q6:

Given that the polar coordinates of point 𝐴 are ( 5 , 3 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ 5 √ 3 2 , 5 2 
  • B ο€Ώ 5 2 , 5 √ 3 2 
  • C ο€Ώ 5 √ 3 2 , βˆ’ 5 2 
  • D ο€Ώ βˆ’ 5 √ 3 2 , βˆ’ 5 2 

Q7:

Given that the polar coordinates of point 𝐴 are ( 6 , 1 2 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€» βˆ’ 3 , 3 √ 3 
  • B ο€» 3 √ 3 , βˆ’ 3 
  • C ο€» βˆ’ 3 , βˆ’ 3 √ 3 
  • D ο€» 3 , βˆ’ 3 √ 3 

Q8:

Given that the polar coordinates of point 𝐴 are ( 3 , 4 5 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ 3 √ 2 2 , 3 √ 2 2 
  • B ο€Ώ βˆ’ 3 √ 2 2 , 3 √ 2 2 
  • C ο€Ώ 3 √ 2 2 , βˆ’ 3 √ 2 2 
  • D ο€Ώ βˆ’ 3 √ 2 2 , βˆ’ 3 √ 2 2 

Q9:

Given that the polar coordinates of point 𝐴 are ( 8 , βˆ’ 6 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€» 4 , βˆ’ 4 √ 3 
  • B ο€» βˆ’ 4 √ 3 , 4 
  • C ο€» 4 , 4 √ 3 
  • D ο€» βˆ’ 4 , 4 √ 3 

Q10:

Given that the polar coordinates of point 𝐴 are ( 5 , βˆ’ 1 3 5 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ βˆ’ 5 √ 2 2 , βˆ’ 5 √ 2 2 
  • B ο€Ώ 5 √ 2 2 , βˆ’ 5 √ 2 2 
  • C ο€Ώ βˆ’ 5 √ 2 2 , 5 √ 2 2 
  • D ο€Ώ 5 √ 2 2 , 5 √ 2 2 

Q11:

Given that the polar coordinates of point 𝐴 are ( 9 , 3 0 ) ∘ , find the Cartesian coordinates of 𝐴 .

  • A ο€Ώ 9 √ 3 2 , 9 2 
  • B ο€Ώ 9 2 , 9 √ 3 2 
  • C ο€Ώ 9 √ 3 2 , βˆ’ 9 2 
  • D ο€Ώ βˆ’ 9 √ 3 2 , βˆ’ 9 2 
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