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The diagram can be organised into diagonal rows, the first at (1,1), the second from (1,2) to (2,1), the third from (3,1) to (1,3) etc. the x and y co-ordinates of the numbers on each line always add up to the same total ( in line (1,4) to (4,1), 4+1 = 3+2 = 2+3 = 1+4 ) this can be used to work out the co-ordinates of the point on the bottom right of the line, because, if you have one point on the line (a,b) you know the bottom right point has co-ordinates (a+b-1,1), because the x and y co-ordinates must add up to the same total. Looking at the diagram you can tell that if the x co-ordinate of the bottom right point on a line is even, the arrows in the line go towards the bottom right, otherwise, they go away. Therefore the point (18,17) is on the line with bottom right point (18+17-1,1) = (34,1). Because 34 is even, the arrows go towards the bottom right, so the next point is (19,16).
The point (9,4) is in the row with bottom right point (9+4-1,1) = (12,1). Therefore, a triangle of dots with corners (1,1), (11,1) and (1,11). It contains (11+10+9...+1) points = 66 points. There are also the dots In the row that (9,4) is in. The bottom right point is (12,1) and 12 is even, so the arrows go towards the bottom right corner. This means there are also points (1,12), (2,11) ... and (8,5) before (9,4) so, there are 66+8= 74 points before (9,4) in the pattern.