WXYZ is a rhombus with vertices W(0,4b), X(2a,0), Y(0,-4), Z(-2,0). You can see thap points W and Y lie on the y-axis and points X and Z lie on the x-axis. Then the centre of the rhombus is origin, thus W and Y are symmetric about the origin. Then b=1 and point W has coordinates (0,4). Similarly points X and Z are symmetric about the origin and a=1, hence X(2,0).
Let KLMN be middlepoints of segments WX, XY, YZ, ZW, respectively. Then
![K( \frac{0+2}{2}, \frac{4+0}{2} )=(1,2) \\ L( \frac{0+2}{2}, \frac{-4+0}{2} )=(1,-2) \\ M( \frac{0-2}{2}, \frac{-4+0}{2} )=(-1,-2) \\ N( \frac{0-2}{2}, \frac{4+0}{2} )=(-1,2)](https://tex.z-dn.net/?f=K%28%20%5Cfrac%7B0%2B2%7D%7B2%7D%2C%20%5Cfrac%7B4%2B0%7D%7B2%7D%20%20%29%3D%281%2C2%29%20%5C%5C%20L%28%20%5Cfrac%7B0%2B2%7D%7B2%7D%2C%20%5Cfrac%7B-4%2B0%7D%7B2%7D%20%20%29%3D%281%2C-2%29%20%5C%5C%20M%28%20%5Cfrac%7B0-2%7D%7B2%7D%2C%20%5Cfrac%7B-4%2B0%7D%7B2%7D%20%20%29%3D%28-1%2C-2%29%20%5C%5C%20N%28%20%5Cfrac%7B0-2%7D%7B2%7D%2C%20%5Cfrac%7B4%2B0%7D%7B2%7D%20%20%29%3D%28-1%2C2%29)
.
Now find the vectors
![\overrightarrow{KL}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BKL%7D)
,
![\overrightarrow{LM}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BLM%7D)
,
![\overrightarrow{MN}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BMN%7D)
and
![\overrightarrow{KN}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BKN%7D)
:
![\overrightarrow{KL}=(1-1,-2-2)=(0,-4) \\ \overrightarrow{KN}=(-1-1,2-2)=(-2,0) \\\overrightarrow{ML}=(-1-1,-2-(-2))=(-2,0) \\ \overrightarrow{MN}=(-1-(-1),2-(-2))=(0,4)\\\overrightarrow{KL}\cdot \overrightarrow{KN}=0\cdot (-2)+(-4)\cdot 0=0](https://tex.z-dn.net/?f=%5Coverrightarrow%7BKL%7D%3D%281-1%2C-2-2%29%3D%280%2C-4%29%20%5C%5C%20%5Coverrightarrow%7BKN%7D%3D%28-1-1%2C2-2%29%3D%28-2%2C0%29%20%5C%5C%5Coverrightarrow%7BML%7D%3D%28-1-1%2C-2-%28-2%29%29%3D%28-2%2C0%29%20%5C%5C%20%5Coverrightarrow%7BMN%7D%3D%28-1-%28-1%29%2C2-%28-2%29%29%3D%280%2C4%29%5C%5C%5Coverrightarrow%7BKL%7D%5Ccdot%20%5Coverrightarrow%7BKN%7D%3D0%5Ccdot%20%28-2%29%2B%28-4%29%5Ccdot%200%3D0)
that means that
![\overrightarrow{KL}\perp \overrightarrow{KN}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BKL%7D%5Cperp%20%5Coverrightarrow%7BKN%7D)
.
Similarly,
![\overrightarrow{LK}\perp \overrightarrow{LM}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BLK%7D%5Cperp%20%5Coverrightarrow%7BLM%7D)
,
![\overrightarrow{ML}\perp \overrightarrow{MN}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BML%7D%5Cperp%20%5Coverrightarrow%7BMN%7D)
,
![\overrightarrow{NM}\perp \overrightarrow{NK}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BNM%7D%5Cperp%20%5Coverrightarrow%7BNK%7D)
.
You prove that KLMN is a recctangle.