Question 1186309
Although I would agree with the arguments of @greenestamps, any student of Euclidean geometry would serve him/her well 
if no assumptions were made based on the diagrams or pictures of the object.  @greenestamps' (and also @ josgarithmetic's) arguments 
hinges on the fact that X, Z, and Y are collinear, which would make angle XZW a RIGHT triangle.  


But this is not completely clear from the drawing, as 
1) Nothing in the hypothesis tells us that the figure WXY is a triangle, and so should not be initially treated as such, and consequently
2) It cannot be assumed that angle XZW is a right angle, because it wasn't stated as a hypothesis -- indeed there was no indication of a "square corner" at angle XZW.  


The remedy is to first show that triangle XZW is a right triangle. 
The easiest way to prove this is to use the fact that the Pythagorean theorem is an "if and only" statement, 
i.e., a triangle is a right triangle if and only if the square of one side is the sum of the squares of the other two sides.

From the given figure side WZ will have length {{{sqrt(15^2 - 9^2) = 12}}}. (We know that triangle WZY is a right triangle.) 
This then will confirm that the sides of triangle XZW satisfy the Pythagorean relation:  {{{5^2 + 12^2 = 13^2}}}, 
and therefore triangle XZW is indeed a right triangle.  And consequently, X, Z, and Y are collinear.