The line segment XZ is the hypotenuse of a right-angled triangle we'll call AXZ, where A is 90 degrees . The point Y is 3/8 along XZ, nearer to X than to Z. By similar triangles the coords of Y will be 3/8 from Y to A and 3/8 from A to Z. AX=AZ=6 (the difference between the x and y coords of points X and Z). 3/8 of 6=9/4=2.25. Take 2.25 from the y value of X: 5-2.25=2.75. The x value for Y is x value of X plus 2.25=1+2.25=3.25. Y is (3.25, 2.75). Another way to look at this is to derive the equation of the line passing through X, Y and Z. The slope is -1, because it's derived from (-1-5)/(7-1)=-6/6=-1. The intercept is found by entering the coords of X or Z into y=-x+b (b is the intercept). Put in X(1,5) and b=6, so y=6-x. The point Y fits on this line. The x value is 3.25.