# Worksheet: Distance and Midpoints on the Complex Plane

In this worksheet, we will practice finding the distance and midpoint of two complex numbers in the complex plane.

Q1:

Find the midpoint of and .

• A
• B
• C
• D
• E

Q2:

A complex number lies at a distance of from and at a distance of from . Is the triangle formed by the points , , and a right triangle?

• AYes
• BNo

Q3:

What is the general form for the midpoint of two complex numbers and ?

• A
• B
• C
• D
• E

Q4:

What complex number lies at the midpoint of the complex numbers and when they are represented on a complex plane?

• A
• B
• C
• D
• E

Q5:

Find the complex number such that lies at the midpoint of and when they are represented on a complex plane.

• A
• B
• C
• D
• E

Q6:

Find the possible real values of such that the distance between the complex number and the complex number is 5.

• A3 or 11
• B1.7 or 15.7
• C5
• D5 or 9
• E0.5 or 14.5

Q7:

What complex number lies at the midpoint of the complex numbers and , where , , , and are real, when they are represented on a complex plane?

• A
• B
• C
• D
• E

Q8:

What is the distance between the complex numbers and , where and are real?

• A
• B
• C
• D
• E

Q9:

What is the distance between the numbers and on the complex plane?

• A1
• B2
• C3
• D4
• E5

Q10:

What is the distance between the numbers and on the complex plane?

• A
• B3
• C4
• D9
• E5

Q11:

What is the distance between the numbers and in the complex plane?

Q12:

What is the distance between the numbers and on the complex plane?

• A4
• B3
• C9
• D
• E

Q13:

Let and be points in the complex plane. A circle of center , where is the complex number , is plotted in the complex plane such that the line is tangential to the circle at point . Point is a distance of from . Given that and , find .

• A
• B
• C
• D
• E

Q14:

What is the distance between the numbers and in the complex plane?

• A
• B
• C12
• D6
• E

Q15:

What is the distance between the numbers and in the complex plane?

Q16:

Let , , and be complex numbers such that lies at the midpoint of the line segment connecting to . Given that and , find .

• A
• B
• C
• D
• E

Q17:

A triangle has its vertices at points , , and in the complex plane. Find an expression for the centroid of the triangle in terms of , , and . You can use the fact that the centroid divides the median in a ratio of .

• A
• B
• C
• D
• E

Q18:

Find the distance between the complex numbers and shown on the complex plane. Give your answer in an exact simplified form. • A4
• B
• C6
• D
• E8

Q19:

Find the distance between the complex numbers and shown on the complex plane. Give your answer in simplified exact form. • A
• B15
• C
• D
• E

Q20:

If , , and , what are the possible values of ?

• A5, 7
• B1, 5
• C, 7
• D, 1
• E5,

Q21:

Find the distance between the complex numbers and shown on the complex plane. • A15
• B
• C
• D
• E

Q22:

Let , , and be complex numbers such that lies at a point on the line that is of the distance from to . Given that and , find .

• A
• B
• C
• D
• E

Q23:

What is the distance between the numbers and 6 on the complex plane? 