Question

If Quadrilateral WXYZ is a rhombus, where points W(-3, 2), X(-2, 6), Y(2, 7) and Z(?, ?) areknown. Find the coordinates of point z

Answer 1

If we consider it in relation to the X-axis, the point X would be the one in the middle. For this reason, the coordinates of Z can be calculated from calculating any displacement from X to Y and adding it to W, or from X to W and adding it to the coordinate of Y. It happens because the opposite sides of a rhombus have the same length and orientation, as follows:

Calculating the displacement from X to Y, which is

$\begin{gathered} d_{x->y}=(x_Y-x_X,y_Y-y_X) \\ d_{x->y}=(2--2,7-6) \\ d_{x->y}=(4,1) \end{gathered}$

Adding it to the W coordinate, we have:

$\begin{gathered} Z=W+d=(x_W+x_d,y_W+y_d) \\ Z=(-3+4,2+1) \\ \\ Z=(1,3) \end{gathered}$

From the solution we developed above, we are able to conclude that the answer to the present question is:

Z = ( 1, 3)