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Lesson: Quadrilaterals on the Coordinate Plane

Sample Question Videos

Worksheet • 12 Questions • 1 Video

Q1:

Consider quadrilateral 𝐴 𝐡 𝐢 𝐷 with vertices 𝐴 ( βˆ’ 2 , 4 ) , 𝐡 ( βˆ’ 4 , 4 ) , 𝐢 ( βˆ’ 1 , βˆ’ 5 ) , and 𝐷 ( 1 , βˆ’ 5 ) . Using the distance formula, determine whether the quadrilateral is a parallelogram.

  • Ano
  • Byes

Q2:

Consider quadrilateral 𝐴 𝐡 𝐢 𝐷 with vertices 𝐴 ( 5 , 4 ) , 𝐡 ( 3 , 5 ) , 𝐢 ( βˆ’ 1 , βˆ’ 5 ) , and 𝐷 ( βˆ’ 3 , βˆ’ 6 ) . Using the distance formula, determine whether the quadrilateral is a parallelogram.

  • Ayes
  • Bno

Q3:

Consider quadrilateral 𝐴 𝐡 𝐢 𝐷 with vertices 𝐴 ( 2 , 2 ) , 𝐡 ( 5 , 3 ) , 𝐢 ( 2 , βˆ’ 1 ) , and 𝐷 ( βˆ’ 1 , βˆ’ 2 ) . Using the distance formula, determine whether the quadrilateral is a parallelogram.

  • Ano
  • Byes

Q4:

Quadrilateral 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( βˆ’ 1 , 7 ) , 𝐡 ( 4 , 4 ) , 𝐢 ( 3 , βˆ’ 3 ) , and 𝐷 ( βˆ’ 2 , 0 ) . Using the midpoint formula, determine whether 𝐴 𝐡 𝐢 𝐷 is a parallelogram.

  • AIt is not a parallelogram.
  • BIt is a parallelogram.

Q5:

Quadrilateral 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( βˆ’ 1 , 7 ) , 𝐡 ( 4 , 4 ) , 𝐢 ( 3 , βˆ’ 3 ) , and 𝐷 ( 8 , 6 ) . Using the midpoint formula, determine whether 𝐴 𝐡 𝐢 𝐷 is a parallelogram.

  • AIt is a parallelogram.
  • BIt is not a parallelogram.

Q6:

Find the area of a quadrilateral with vertices 𝐴 ( βˆ’ 1 2 , βˆ’ 5 ) , 𝐡 ( βˆ’ 9 , βˆ’ 9 ) , 𝐢 ( βˆ’ 4 , βˆ’ 9 ) , and 𝐷 ( βˆ’ 7 , βˆ’ 5 ) .

Q7:

Find the perimeter and the area of the quadrilateral whose vertices are 𝑇 ( 4 , βˆ’ 2 ) , π‘ˆ ( 1 0 , 4 ) , 𝑉 ( 1 4 , 0 ) , and π‘Š ( 8 , βˆ’ 6 ) . If necessary, round your answers to the nearest tenth.

  • Aperimeter = 2 8 . 3 , area = 4 8
  • Bperimeter = 4 0 . 8 , area = 2 0
  • Cperimeter = 1 4 . 1 , area = 4 8
  • Dperimeter = 4 0 . 8 , area = 1 0 4
  • Eperimeter = 2 8 . 3 , area = 1 4

Q8:

Find the perimeter and area of the quadrilateral whose vertices are 𝑃 ( βˆ’ 4 , 0 ) , 𝑄 ( 5 , 1 2 ) , 𝑅 ( 1 7 , 3 ) , and 𝑆 ( 8 , βˆ’ 9 ) .

  • Aperimeter = 6 0 , area = 2 2 5
  • Bperimeter = 3 6 , area = 8 1
  • Cperimeter = 6 0 , area = 3 0
  • Dperimeter = 4 2 , area = 1 0 8
  • Eperimeter = 4 5 , area = 2 2 5

Q9:

A quadrilateral has vertices at the points 𝐴 ( 0 , 5 ) , 𝐡 ( 2 , 6 ) , 𝐢 ( 4 , 2 ) , and 𝐷 ( 2 , 1 ) .

Work out the slope of the four edges of the quadrilateral.

  • A Slope 𝐴 𝐡 = 1 2 , 𝐡 𝐢 = βˆ’ 2 , 𝐢 𝐷 = 1 2 , 𝐴 𝐷 = βˆ’ 2 s l o p e s l o p e s l o p e
  • B Slope 𝐴 𝐡 = βˆ’ 1 2 , 𝐡 𝐢 = 2 , 𝐢 𝐷 = βˆ’ 1 2 , 𝐴 𝐷 = 2 s l o p e s l o p e s l o p e
  • C Slope 𝐴 𝐡 = 1 1 2 , 𝐡 𝐢 = 4 3 , 𝐢 𝐷 = 2 , 𝐴 𝐷 = 1 2 s l o p e s l o p e s l o p e
  • D Slope 𝐴 𝐡 = 2 , 𝐡 𝐢 = βˆ’ 1 2 , 𝐢 𝐷 = 4 3 , 𝐴 𝐷 = 3 s l o p e s l o p e s l o p e
  • E Slope 𝐴 𝐡 = 2 1 1 , 𝐡 𝐢 = 3 4 , 𝐢 𝐷 = βˆ’ 2 , 𝐴 𝐷 = βˆ’ 1 2 s l o p e s l o p e s l o p e

By finding the product of the slope, can we know if the quadrilateral is a rectangle?

  • Ano
  • Byes

Q10:

A zoo plotted a map of its exhibits on the coordinate plane where each unit represented 1 ft. The vertices of the lion's enclosure were at ( 1 0 , 6 0 ) , ( 7 0 , 6 0 ) , ( 5 0 , 2 0 ) , and ( 1 0 , 2 0 ) . Find the area of the lion's enclosure.

Q11:

A quadrilateral has vertices at the points 𝐴 ( 0 , 5 ) , 𝐡 ( 1 , 7 ) , 𝐢 ( 4 , 5 ) , and 𝐷 ( 2 , 1 ) .

Work out the slope of the four edges of the quadrilateral.

  • A Slope of 𝐴 𝐡 = 2 , Slope of 𝐡 𝐢 = βˆ’ 2 3 , Slope of 𝐢 𝐷 = 2 , Slope of 𝐴 𝐷 = βˆ’ 2
  • B Slope of 𝐴 𝐡 = 1 1 1 , Slope of 𝐡 𝐢 = 1 2 5 , Slope of 𝐢 𝐷 = 2 , Slope of 𝐴 𝐷 = βˆ’ 1 2
  • C Slope of 𝐴 𝐡 = 1 1 , Slope of 𝐡 𝐢 = βˆ’ 3 2 , Slope of 𝐢 𝐷 = 2 , Slope of 𝐴 𝐷 = 3
  • D Slope of 𝐴 𝐡 = 1 2 , Slope of 𝐡 𝐢 = 3 2 , Slope of 𝐢 𝐷 = 2 , Slope of 𝐴 𝐷 = 2
  • E Slope of 𝐴 𝐡 = 0 , Slope of 𝐡 𝐢 = 2 3 , Slope of 𝐢 𝐷 = 2 , Slope of 𝐴 𝐷 = βˆ’ 3

What type of shape is 𝐴 𝐡 𝐢 𝐷 ?

  • Atrapezium
  • Brhombus
  • Cparallelogram
  • Dsquare
  • Erectangle

Q12:

A factory plotted its building on a map using a coordinate plane where each unit represented 1 m. The vertices of one of the buildings were plotted at ( 2 0 , 1 0 ) , ( 2 0 , 5 0 ) , ( 5 0 , 5 0 ) , ( 7 0 , 7 0 ) , and ( 7 0 , 1 0 ) . Find the area of the building.

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