Question

Wany words does that message have?

Answer 1

Answer:

  (4, 3)

Explanation:

Short answer: when the coordinates are on horizontal and vertical lines, as these are, each coordinate value is used twice. Already, x=0 is used twice, as is y=0, so the missing coordinate is x=4, y=3.

The fourth vertex is (4, 3).

_____

Longer answer: The midpoints of the diagonals are the same point, so for rectangle ABCD, we have ...

  (A+C)/2 = (B+D)/2

Solving for D, we find ...

  D = A +C -B

In clockwise order, the points given are ...

  A = (4, 0), B = (0, 0), C = (0, 3)

so we have ...

  D = (4, 0) +(0, 3) -(0, 0) = (4+0-0, 0+3-0)

  D = (4, 3) . . . . the coordinates of the fourth vertex.