AQA · Mathematics · 8300

GCSE Maths: Coordinates: 3D

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Coordinates: 3D (Corbettmaths Video 86), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

9 flashcards · Free to study · No account needed

Study this deck

Preparing your cards…

All questions and answers

Read through the full deck, or practise recalling each answer above.

In 3D coordinate geometry, how many coordinates are needed to specify a point in space?
Show answer
Three coordinates (x, y, z).
A cuboid is a ? shape with six rectangular faces.
Show answer
3D rectangular
If a cuboid has one vertex at the origin (0, 0, 0) and an opposite vertex at (a, b, c), what are the coordinates of the vertex directly above the origin?
Show answer
(0, 0, c). The z-coordinate changes while x and y remain zero.
What is the formula for the midpoint of a line segment joining points (x₁, y₁, z₁) and (x₂, y₂, z₂)?
Show answer
((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). Average each coordinate separately.
In a cube where one edge runs from (7, 0, 0) to (12, 0, 0), what is the edge length?
Show answer
5 units. The distance is |12 - 7| = 5.
If point P divides line segment EF in the ratio 2:3 starting from E, and E is at position 0 and F at position 5 along an axis, where is P?
Show answer
At position 2. P is 2/(2+3) = 2/5 of the way from E to F, so 0 + 2/5×5 = 2.
What is the distance formula between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in 3D space?
Show answer
√[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]. The 3D extension of the Pythagorean theorem.
In a cuboid aligned with coordinate axes, if one vertex is at (0, 0, 0) and the opposite corner is at (6, 20, 8), how many distinct vertices does the cuboid have?
Show answer
8 vertices. A cuboid always has 8 corners.
If a cuboid has edges parallel to the coordinate axes and one vertex at (0, 0, 0) with dimensions 6×20×8, what are the coordinates of the opposite vertex?
Show answer
(6, 20, 8). Each coordinate equals the dimension along that axis.

Want to create your own cards? Create a free account. AI generation uses credits.

Study this deck

All questions and answers

In 3D coordinate geometry, how many coordinates are needed to specify a point in space?

A cuboid is a ? shape with six rectangular faces.

If a cuboid has one vertex at the origin (0, 0, 0) and an opposite vertex at (a, b, c), what are the coordinates of the vertex directly above the origin?

What is the formula for the midpoint of a line segment joining points (x₁, y₁, z₁) and (x₂, y₂, z₂)?

In a cube where one edge runs from (7, 0, 0) to (12, 0, 0), what is the edge length?

If point P divides line segment EF in the ratio 2:3 starting from E, and E is at position 0 and F at position 5 along an axis, where is P?

What is the distance formula between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in 3D space?

In a cuboid aligned with coordinate axes, if one vertex is at (0, 0, 0) and the opposite corner is at (6, 20, 8), how many distinct vertices does the cuboid have?

If a cuboid has edges parallel to the coordinate axes and one vertex at (0, 0, 0) with dimensions 6×20×8, what are the coordinates of the opposite vertex?