# Worksheet: Points, Midpoints, and Distances in Space

In this worksheet, we will practice finding the coordinates of a point in 3D, the distance between two points in 3D, and the coordinates of a midpoint and an endpoint in 3D using the formula.

**Q1: **

Given that the midpoint of lies in the -plane, and the coordinates of and are and , respectively, determine the value of .

- A
- B
- C
- D

**Q3: **

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of , given that the coordinates of , , and are , , and , respectively.

**Q4: **

Given that point is the midpoint of and that , what are the coordinates of ?

- A
- B
- C
- D

**Q5: **

Given that point is the midpoint of and that , what are the coordinates of ?

- A
- B
- C
- D

**Q6: **

Given that point is the midpoint of and that , what are the coordinates of ?

- A
- B
- C
- D

**Q7: **

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of , given that the coordinates of , , and are , , and , respectively.

**Q8: **

Given that the midpoint of lies in the -plane, and the coordinates of and are and , respectively, determine the value of .

- A
- B
- C
- D

**Q9: **

Given that the midpoint of lies in the -plane, and the coordinates of and are and , respectively, determine the value of .

- A
- B
- C
- D

**Q10: **

In which of the following coordinate planes does the point lie?

- A
- B
- C

**Q11: **

Given that the point lies in the -plane, determine its -coordinate.

**Q12: **

Given that the point lies in the -plane, determine its -coordinate.

**Q13: **

Given that the point lies in the -plane, determine its -coordinate.

**Q15: **

Given that the point lies in the -plane, what is this point?

- A
- B
- C
- D

**Q17: **

What is the distance between the point and the -axis?

- A19 length units
- B length units
- C length units
- D length units

**Q19: **

The points , , and are on the -, -, and -axes, respectively. Given that is the midpoint of and the midpoint of , find the coordinates of the midpoint of .

- A
- B
- C
- D

**Q20: **

Given that is the midpoint of , where the coordinates of and are and , respectively, what is ?

**Q21: **

Given that point lies in the -plane, determine its distance from the -plane.

**Q22: **

Given that is the midpoint of the line segment between and , what is ?

- A
- B
- C
- D

**Q24: **

Find so that the points , , are collinear.

**Q25: **

Given that the points , , and are the vertices of a triangle, determine all the possible values of that make the triangle equilateral.

- A
- B
- C
- D