Question

Consider the three points graphed. What is the value of y in the fourth point that will complete the quadrilateral as a rhombus?

(–1,

Answer 1

I can do that, but the problem statement you pasted is cut off — I only see "(−1," and not the other coordinates. Could you paste the three full points or the graph?

Meanwhile, here is the quickest way to get the missing vertex of a rhombus once you have three vertices:

- Label the three known vertices A(x1,y1), B(x2,y2), C(x3,y3). If A and C are opposite vertices of the rhombus (so the missing vertex D is opposite B), then the diagonals bisect each other, so the midpoints of AC and BD are equal. That gives
D = A + C − B,
i.e. D(xD,yD) = (x1 + x3 − x2,\; y1 + y3 − y2).

- If instead the three given points are three consecutive vertices A, B, C (so the missing vertex D closes the quadrilateral after C), then the same vector fact holds: D = A + C − B.

So paste the three coordinates and I’ll compute y (and the full D) for you.