# 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:

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

Q3:

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

• A
• B8
• 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

Q8:

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

Q9:

If , , , and are vertices of the trapezoid , find the value of using vectors.

Q10:

If , , and are vertices of the triangle , find the coordinates of the point of intersection of its medians using vectors.

• A
• B
• C
• D
• E