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 𝐴𝐵𝐶, 𝐴𝐵+𝐵𝐶=.

  • A𝐵𝐴
  • B𝐶𝐵
  • C𝐴𝐶
  • D𝐶𝐴
  • E𝐴𝐵


Fill in the blank: In the parallelogram 𝐴𝐵𝐶𝐷, 𝐴𝐵+𝐴𝐷=.

  • A𝐴𝐶
  • B𝐶𝐷
  • C𝐵𝐷
  • D𝐶𝐴
  • E𝐵𝐶


Which of the following is equivalent to 𝐴𝐵𝐷𝐵?

  • A𝐵𝐴
  • B𝐴𝐶
  • C𝐵𝐶
  • D𝐷𝐶
  • E𝐷𝐴


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

  • A67
  • B12
  • C12
  • D67


In the triangle 𝐴𝐵𝐶, 𝐷𝐵𝐶, where 𝐵𝐷𝐷𝐶=23. Given that 3𝐴𝐵+2𝐴𝐶=𝑘𝐴𝐷, find the value of 𝑘.


Trapezoid 𝐴𝐵𝐶𝐷 has vertices 𝐴(4,14), 𝐵(4,4), 𝐶(12,4), and 𝐷(12,9). Given that 𝐴𝐵𝐷𝐶 and 𝐴𝐵𝐶𝐵, find the area of that trapezoid.


𝐴𝐵𝐶𝐷 is a rectangle, in which the coordinates of the points 𝐴, 𝐵, and 𝐶 are (18,2), (18,3), and (8,𝑘), respectively. Use vectors to find the value of 𝑘 and the coordinates of point 𝐷.

  • A𝑘=1, 𝐷(8,3)
  • B𝑘=2, 𝐷(28,2)
  • C𝑘=3, 𝐷(8,2)
  • D𝑘=1, 𝐷(28,2)
  • E𝑘=2, 𝐷(8,2)


Complete the following: If 𝐴𝐵𝐶𝐷 is a quadrilateral and 𝐴𝐷=𝐵𝐶 and they are parallel, then the quadrilateral can always be classified as .

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


𝐴𝐵𝐶𝐷 is a quadrilateral in which 𝐴(1,2), 𝐵(1,3), 𝐶(5,3), and 𝐷(5,2). Determine its type using vectors.

  • AParallelogram
  • BRectangle
  • CKite
  • DTrapezoid


𝐴𝐵𝐶𝐷 is a square, in which the coordinates of the points 𝐴, 𝐵, and 𝐶 are (1,8), (3,10), and (5,8). Use vectors to determine the coordinates of the point 𝐷 and the area of the square.

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

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