# 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

Q2:

Points , have coordinates and , respectively. Determine the coordinates of the midpoint 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 .

Q13:

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

Q14:

Determine the coordinates of point . • A
• B
• C
• D

Q15:

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

• A
• B
• C
• D

Q16:

In the figure shown, the points and have coordinates and , respectively. Determine the coordinates of and . • 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

Q18:

Calculate, to two decimal places, the area of the triangle , where the coordinates of its vertices are at , , and .

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

Q23:

Find the distance between the two points and .

• Alength units
• Blength units
• Clength units
• Dlength units

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