A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. What is the y- coordinate of the fourth vertex? h j k

QUESTION POSTED AT 18/04/2020 - 05:52 PM

Answered by admin AT 18/04/2020 - 05:52 PM

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})

By comparing the y-coordinates,

\frac{j+0}{2}=\frac{0+y}{2}

\implies y=j

Hence, the y-coordinate of the fourth vertex is j.

Second option is correct.

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