On the xy – plane, find the number of triangles whose vertices have integer coordinates (x, y) satisfying 1 ≤ x ≤ 3 and 1 ≤ y ≤ 3?
Answers
Answered by
1
Given : triangles whose vertices have integer coordinates (x, y) satisfying 1 ≤ x ≤ 3 and 1 ≤ y ≤ 3
To Find : Number of Triangles
Solution:
1 ≤ x ≤ 3 and 1 ≤ y ≤ 3
=> x = { 1 , 2 , 3}
y = { 1 , 2 , 3}
( x, y) = 3 * 3 = 9
Hence total 9 points
3 points out of 9 points can be selected in ⁹C₃ ways
= 84
But this contains the straight lines also
There would be 8 straight lines
Hence 84 - 8 = 76 Triangles are possible
Learn More:
https://brainly.in/question/5771768
how many Triangles are there in a heptagon if drawn from a single ...
how many triangles can be formed with 10 points in a plane of which ...
https://brainly.in/question/5768984
Similar questions