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As you go from X to Z, the x coordinate goes 7 -> -3 (a decrease of 10), and the y-coordinate goes 2 -> -3 (a decrease of 5).
XY:YZ is 2:3, so XY is 2/(2+3) or 40% of the length of XZ. The x- and y-coordinates will drop by (40%)(10) and (40%)(5) respectively, as you move from X to Y; so the coordinates at Y will be
(x-coord of X - (0.4)(10), y-coord of X - (0.4)(5))
= ( 7 - 4, 2 - 2)
= (3, 0)
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