ABC is an equilateral triangle .Three distinct points are marked on each sides of the triangle. (not on the vertices). (i) How m

Question

2 years ago

9

ABC is an equilateral triangle .Three distinct points are marked on each sides of the triangle. (not on the vertices). (i) How m

any 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]

Mathematics

1 answer:

iVinArrow [24] · Answer 1 · 2023-04-01T07:21:19+03:00

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

<h3>The number of lines that can be drawn</h3>

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

<h3>The number of triangles that can be drawn</h3>

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