Question

A friend of Steve who is a gardener is dealing with some issues about planting seeds. It turns out that she has a square garden and decided to plant seeds of beautiful flowering plants at these following particular locations. Now, she wants to plant a seed at $F$ which lies exactly between $C$ and $D$. What are the coordinates of $F$?

• A. $(5,2)$
• B. $(4,-2)$
• C. $(5,4)$
• D. $(5,-2)$

Answer 1

The correct option is D $(5,-2)$


From the above figure, it is clear that the coordinates of $C$ and $D$ are $(5,0)$ and $(5,-4)$, respectively.

Both $C$ and $D$ have same $x$-coordinate value as $5$ but $D$ is $4$ units down to the $C$. Hence, $C$ and $D$ lie on the line $x=5$. We need to find out the point $F$, which is exactly in-between $C$ and $D$.


As $F$ should lie within the line segment $CD$, the $x$-coordinate of $F$ must be equal to the $x$-coordinate of $C$ and $D$, i.e., $5$. And, as $F$ is exactly in the middle of $CD$, the $y$-coordinate lies in the middle of $0$ ($y$-coordinate of $C$) and $-4$ ($y$-coordinate of $D$), which is definitely be $-2$.

$\therefore$ The coordinates of $F$ are $(5,-2)$.