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ABC is an equilateral triangle .Three distinct points are marked on each sides of the triangle. (not on the vertices). (i) How many lines can be drawn joining 2 of these nine points? [3 marks] (ii) Find the number of different triangles that can be formed using of 3 of these nine points as vertices. [3 marks]

Sagot :

MrRoyal

The number of lines and triangles illustrates combination

  • 36 lines can be drawn to join the nine points
  • 84 triangles can be drawn using the nine points

The number of lines that can be drawn

The given parameters are:

Total points, n = 9

Total points on each line, r = 2

The number of lines that can be drawn is then calculated  using the following combination formula

Lines = nCr

This gives

Lines = 9C2

Evaluate the combination expression

Lines = 36

Hence, 36 lines can be drawn to join the nine points

The number of triangles that can be drawn

The given parameters are:

Total points, n = 9

Total points on each triangle, r = 3

The number of triangles that can be drawn is then calculated  using the following combination formula

Triangles = nCr

This gives

Triangles = 9C3

Evaluate the combination expression

Triangles = 84

Hence, 84 triangles can be drawn using the nine points

Read more about combination at:

https://brainly.com/question/11732255

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