Question

In rectangle $OABC$; point $O$ is the origin, $OA=10$ units along $x$-axis and $AB=8$ units. Find the co-ordinates of vertices $A,B$ and $C$.

• A. $A=(10,0),B=(10,8)$ and $C=(0,8)$
• B. $A=(10,0),C=(10,8)$ and $B=(0,8)$
• C. $B=(10,0),A=(10,8)$ and $C=(0,8)$
• D. $B=(10,0),C=(10,8)$ and $A=(0,8)$

Answer 1

The correct option is A $A=(10,0),B=(10,8)$ and $C=(0,8)$

We plot the point Origin $O$. Now, we move $10$ units to the right on the $x$-axis and mark it as point $A(10,0)$.
Since $OABC$ is a rectangle, $AB$ will be perpendicular to $OA$. So, we move $8$ units upwards from $A$, and mark the point as $B(10,8)$.

Since opposite sides of the rectangle are equal , $OA=BC$ therefore move $10$ units to the left parallel to $OA$
Now we join $OA,AB$ and $BC$ with straight lines and complete the rectangle $OABC$. Hence, we obtain point $C(0,8)$.

Therefore, the coordinates $A,B$ and $C$ are $(10,0),(10,8)$ and $(0,8)$, respectively.

Hence, option $A$ is correct.