Properties of TriangleHard
Question
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is :
Options
A.820
B.780
C.901
D.861
Solution
Let P be (x, y) x ≥1 y ≥ 1
∴ y + y < 41
x + y ≤ 40
x + y + t = 40, t ≥ 0
(x − 1) + (y − 1) + t = 38
∴ No. of points = 38+3−1C3-1
= 40C2 = 780
∴ y + y < 41
x + y ≤ 40
x + y + t = 40, t ≥ 0
(x − 1) + (y − 1) + t = 38
∴ No. of points = 38+3−1C3-1
= 40C2 = 780
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