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Lesson Worksheet: Geometric Applications of Vectors Mathematics

In this worksheet, we will practice using vector operations and vector properties to solve problems involving geometrical shapes.


Fill in the blank: In triangle 𝐴𝐡𝐢, 𝐴𝐡+οƒŸπ΅πΆ=.

  • A𝐡𝐴
  • BοƒŸπΆπ΅
  • C𝐴𝐢
  • D𝐢𝐴
  • E𝐴𝐡


Fill in the blank: In the parallelogram 𝐴𝐡𝐢𝐷, 𝐴𝐡+𝐴𝐷=.

  • A𝐴𝐢
  • B𝐢𝐷
  • C𝐡𝐷
  • D𝐢𝐴
  • EοƒŸπ΅πΆ


Which of the following is equivalent to οƒ π΄π΅βˆ’οƒ π·π΅?

  • A𝐡𝐴
  • B𝐴𝐢
  • CοƒŸπ΅πΆ
  • D𝐷𝐢
  • E𝐷𝐴


Given the information in the diagram below, find the value of 𝑛 such that 𝐴𝐷+𝐷𝐸=𝑛𝐴𝐢.

  • A67
  • B12
  • Cβˆ’12
  • Dβˆ’67


In the triangle 𝐴𝐡𝐢, 𝐷∈𝐡𝐢, where 𝐡𝐷∢𝐷𝐢=2∢3. Given that 3𝐴𝐡+2𝐴𝐢=π‘˜οƒ π΄π·, find the value of π‘˜.


Trapezoid 𝐴𝐡𝐢𝐷 has vertices 𝐴(4,14), 𝐡(4,βˆ’4), 𝐢(βˆ’12,βˆ’4), and 𝐷(βˆ’12,9). Given that 𝐴𝐡βˆ₯𝐷𝐢 and οƒ π΄π΅βŸ‚οƒŸπΆπ΅, find the area of that trapezoid.


𝐴𝐡𝐢𝐷 is a rectangle, in which the coordinates of the points 𝐴, 𝐡, and 𝐢 are (βˆ’18,βˆ’2), (βˆ’18,βˆ’3), and (βˆ’8,π‘˜), respectively. Use vectors to find the value of π‘˜ and the coordinates of point 𝐷.

  • Aπ‘˜=βˆ’1, 𝐷(βˆ’8,βˆ’3)
  • Bπ‘˜=βˆ’2, 𝐷(βˆ’28,βˆ’2)
  • Cπ‘˜=βˆ’3, 𝐷(βˆ’8,βˆ’2)
  • Dπ‘˜=βˆ’1, 𝐷(βˆ’28,βˆ’2)
  • Eπ‘˜=βˆ’2, 𝐷(βˆ’8,βˆ’2)


Complete the following: If 𝐴𝐡𝐢𝐷 is a quadrilateral and 𝐴𝐷=οƒŸπ΅πΆ and they are parallel, then the quadrilateral can always be classified as .

  • Aa kite
  • Ba parallelogram
  • Ca trapezoid
  • Da rectangle
  • Ean isosceles trapezoid


𝐴𝐡𝐢𝐷 is a quadrilateral in which 𝐴(1,2), 𝐡(1,3), 𝐢(5,3), and 𝐷(5,2). Determine its type using vectors.

  • AParallelogram
  • BRectangle
  • CKite
  • DTrapezoid


𝐴𝐡𝐢𝐷 is a square, in which the coordinates of the points 𝐴, 𝐡, and 𝐢 are (1,βˆ’8), (3,βˆ’10), and (5,βˆ’8). Use vectors to determine the coordinates of the point 𝐷 and the area of the square.

  • A𝐷(3,βˆ’6), area =8
  • B𝐷(1,10), area =340
  • C𝐷(9,βˆ’26), area =16
  • D𝐷(7,βˆ’10), area =8

This lesson includes 31 additional questions and 155 additional question variations for subscribers.

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