+64 A lattice point is an ordered pair (x, y) where both x and y are integers. A triangle is formed
by the three points (1, 1), (9, 1), and (9, n). For what integer value of n > 0 are there exactly 560 lattice
points strictly in the interior of the triangle?
(Yes I know I posted this one a few days ago, but the only answer I got was from a guest who didn't show their work and didn't get the correct answer... so for the people answering this one, please show your work.)
Complete the rectangle.
Discounting the boundary, there will be 7 verticals and n - 2 horizontals producing a total of 7(n - 2) lattice points.
Assuming for the moment that there are no lattice points on the diagonal, we need 7( n -2) = 2×560, so n = 162.
Check now that with n = 162 there are no lattice points on the diagonal meaning that there will be 560 lattice points within each of the two triangles.
