# Worksheet: Distance between Two Points in Three Dimensions

In this worksheet, we will practice finding the coordinates of a point in three dimensions, the plane in which it is located, and the distance between two points.

Q1:

Find the distance between the two points and .

• A length units
• B length units
• C length units
• D length units

Q2:

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

• A
• B
• C
• D

Q3:

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

Q4:

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

Q5:

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

Q6:

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

• A length units
• B19 length units
• C length units
• D length units

Q7:

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

Q8:

Find so that the points , , are collinear.

Q9:

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

Q10:

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