# 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.

**Q1: **

Fill in the blank: In triangle , .

- A
- B
- C
- D
- E

**Q2: **

Fill in the blank: In the parallelogram , .

- A
- B
- C
- D
- E

**Q3: **

Which of the following is equivalent to ?

- A
- B
- C
- D
- E

**Q4: **

Given the information in the diagram below, find the value of such that .

- A
- B
- C
- D

**Q5: **

In the triangle , , where . Given that , find the value of .

**Q6: **

Trapezoid has vertices , , , and . Given that and , find the area of that trapezoid.

**Q7: **

is a rectangle, in which the coordinates of the points , , and are , , and , respectively. Use vectors to find the value of and the coordinates of point .

- A,
- B,
- C,
- D,
- E,

**Q8: **

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

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

**Q9: **

is a quadrilateral in which , , , and . Determine its type using vectors.

- AParallelogram
- BRectangle
- CKite
- DTrapezoid

**Q10: **

is a square, in which the coordinates of the points , , and are , , and . Use vectors to determine the coordinates of the point and the area of the square.

- A, area
- B, area
- C, area
- D, area