# Worksheet: Geometric Applications of Vectors

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

**Q1: **

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

**Q2: **

Trapezium has vertices , , , and . Given that and , find the area of that trapezium.

**Q3: **

Given a trapezium , in which and , find the value of such that .

- A8
- B
- C
- D

**Q4: **

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 ,

**Q5: **

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

- A
- B
- C
- D

**Q6: **

Given a triangle , in which , , and , use vectors to determine the length of .

- A cm
- B cm
- C cm
- D cm

**Q7: **

Given that , , , and are four collinear points, where , determine the value of which satisfies .

- A
- B
- C