As the question is unclear, we do not know whether to count the points (1,1) and (9,4). First, let's assume that we do count these points. As the shape that the journey takes turns out to be a right-angled triangle, we find out what line would take us to the point (9,4). You do not have to draw out the whole journey to do this; you just draw a grid and draw a line through the point (9,4). Then you take a look at where the y-intercept of the line is. This is 12. The triangle goes down one y coordinate each time so to find out the number of points we do: 12+11+10+9+8+7+6+5+4+3+2+1. This isn't the full equation because when you draw the line mentioned above, the point (9,4) is not at the end of the line. There are three points after it, so the full equation is: 12+11+10+9+8+7+6+5+4+3+2+1-3. This gives you 75.
On the other hand, if we are not supposed to count the points (1,1) and (9,4), then we just subtract another two from the equation because there are two of these points. The equation becomes: 12+11+10+9+8+7+6+5+4+3+2+1-3-2.