# Worksheet: Equations of Parallel and Perpendicular Planes

In this worksheet, we will practice finding the equation of a plane that is parallel or perpendicular to another plane given its equation or some properties.

Q1:

and are two parallel planes, where is a point between the two planes. Two straight lines are drawn from the point such that one intersects the planes and at points and respectively, and the other intersects the planes and at points and respectively. If and the surface area of , find the surface area of .

Q2:

and are two parallel planes, and , , and are drawn to intersect the plane at the points , , and , respectively, and the plane at the points , , and , respectively, where the point doesn’t belong to any of the planes. Given that , , , and , determine the area of the .

Q3:

Given that the plane is parallel to the plane , find the values of and .

• A,
• B,
• C,
• D,

Q4:

,, and are three parallel planes intersected by two coplanar straight lines and , where . If , find the length of . Q5:

,, and are three parallel planes intersected by two coplanar straight lines and such that . If , find the length of . Q6:

Given that the plane is perpendicular to the plane , find the value of .

Q7:

Two 3D shapes lie between two parallel planes. Any other plane which is parallel to the two planes intersects both shapes in regions of the same area. What can you deduce about the shapes?

• AThey have the same volume.
• BThey are both prisms.
• CThey are similar.
• DThey have the same surface area.
• EThey are congruent.

Q8:

Determine the general equation of the plane that contains the straight line and that is perpendicular to the plane .

• A
• B
• C
• D
• E

Q9:

Find the general equation of the plane which passes through the point and is perpendicular to the two planes and .

• A
• B
• C
• D
• E

Q10:

Find the equation of the plane passing through the point and parallel to the plane .

• A
• B
• C
• D
• E

Q11:

Find the general form of the equation of the plane that passes through the two points and and that is perpendicular to the plane .

• A
• B
• C
• D
• E

Q12:

Find the general form of the equation of the plane passing through the point and parallel to the plane .

• A
• B
• C
• D
• E

Q13:

Find the general equation of the plane that is perpendicular to the plane and cuts the - and -axes at and respectively.

• A
• B
• C
• D
• E

Q14:

Determine if the planes and are parallel or perpendicular.

• AParallel
• BPerpendicular

Q15:

Determine if the planes and are parallel or perpendicular.

• APerpendicular
• BParallel

Q16:

Determine whether the planes and are parallel or perpendicular.

• AParallel
• BPerpendicular

Q17:

Determine whether the planes and are parallel or perpendicular.

• AParallel
• BPerpendicular

Q18:

Determine whether the planes and are parallel or perpendicular.

• APerpendicular
• BParallel

Q19:

Determine whether the planes and are parallel or perpendicular.

• APerpendicular
• BParallel

Q20:

Determine whether the planes and are parallel or perpendicular.

• APerpendicular
• BParallel

Q21:

Determine whether the planes and are parallel or perpendicular.

• AParallel
• BPerpendicular

Q22:

Determine whether the planes and are parallel or perpendicular.

• AParallel
• BPerpendicular