# 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.

**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

**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.

Give your answer in simplified exact form.

- 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?