A cube has 8 vertices. For each pair of distinct vertices, we connect them up with a line segment. There are (8 2 )=28 such line segments. For each of these 28 line segments, we mark the midpoint. How many distinct points have been marked as the midpoints?

Question

A cube has 8 vertices. For each pair of distinct vertices, we connect them up with a line segment. There are (8 2 )=28 such line segments. For each of these 28 line segments, we mark the midpoint. How many distinct points have been marked as the midpoints?

Answer 1

which of the numbers below is the sum of four consecutive whole numbers

Answer 2

To find the number of distinct points that have been marked as midpoints, we need to consider the number of line segments connecting each pair of distinct vertices on a cube.

A cube has 8 vertices, and we need to choose 2 vertices at a time to connect them with a line segment. This can be calculated using the combination formula:

(8 choose 2) = 8! / (2! * (8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28

So, there are 28 distinct line segments in total on a cube.

For each of these 28 line segments, we mark the midpoint. Therefore, the number of distinct points that have been marked as midpoints is also 28.

Hence, there are 28 distinct points marked as the midpoints on a cube.

A cube has 8 vertices. For each pair of distinct vertices, we connect them up with a line segment. There are (8 2 )=28 such line segments. For each of these 28 line segments, we mark the midpoint. How many distinct points have been marked as the midpoints?

19

which of the numbers below is the sum of four consecutive whole numbers

To find the number of distinct points that have been marked as midpoints, we need to consider the number of line segments connecting each pair of distinct vertices on a cube.