What is the value of x and y in terms of k

Hi vatsavayi,

First, we are going to assume the question asks for x and y in terms of k, a, and b. Questions on the GMAT won't be worded poorly. The best way to solve this problem is by diving in.

We know that y = a - k because y is the height from the x-axis to the point (x,y), which is also the height from the origin to the point (0,a-k). The diagram shows how y + k = a. The only answer choice that has solution for y is B.

Next, we want to find x. Because the two triangles share the angle created at (0,a), we know we have two similar triangles. One of the properties of similar triangles is that their side lengths will be proportional. See the diagram to help visualize this. Thus, x/k = b/a. With a little algebra we can see that x = bk/a.

Answer choice B correctly shows both these solutions and is therefore the right answer. If you want to learn more about similar triangles, here is a good link: https://www.mathsisfun.com/geometry/tria ... milar.html, or you can feel free to reach out/ ask more questions.

Hope this helps! Good luck studying!