Answer:
The y-coordinate of the fourth vertex is j.
Step-by-step explanation:
Since, the diagonals of parallelogram bisect each othe,
That is, the midpoint of one diagonal = the midpoint of the other diagonal,
Here, the consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0,
Let (x,y) are the coordinates of fourth vertex,
⇒ Midpoint of coordinates (h, j) and (k, 0) = Midpoint of coordinate (0,0) and (x,y)
![\implies (\frac{h+k}{2}, \frac{j+0}{2})=(\frac{0+x}{2},\frac{0+y}{2})](https://tex.z-dn.net/?f=%5Cimplies%20%28%5Cfrac%7Bh%2Bk%7D%7B2%7D%2C%20%5Cfrac%7Bj%2B0%7D%7B2%7D%29%3D%28%5Cfrac%7B0%2Bx%7D%7B2%7D%2C%5Cfrac%7B0%2By%7D%7B2%7D%29)
By comparing the y-coordinates,
![\frac{j+0}{2}=\frac{0+y}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bj%2B0%7D%7B2%7D%3D%5Cfrac%7B0%2By%7D%7B2%7D)
![\implies y=j](https://tex.z-dn.net/?f=%5Cimplies%20y%3Dj)
Hence, the y-coordinate of the fourth vertex is j.
Second option is correct.