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?

Chandalier Oct 26, 2022

#2**+1 **

The first think I would do is start drawing triangles on some grid paper.

They way maybe I can come up with some formula for this.

Have you tried that? Or have you thought of anything else?

Melody Nov 4, 2022

#3**+1 **

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?

**I'm quite sure there is a better way to do this**

but

First I translated the points to (0,0), (8,0) and (8,n) n>=0 because i thought it sould be easier

then drew up a dot grid and counted the number of __extra__ dots each time n increased by 1

this looks like a pattern, assuming that it continues this way ...

560/28 = 20

20+1=21

I think the answer is 21 ....

Melody Nov 5, 2022