Question

In the $xy$-coordinate plane, the coordinates of three vertices of a rectangle are $(1,5)$, $(5,2)$ and $(5,5)$. What are the coordinates of the fourth vertex of the rectangle?

• A. $(1,2)$
• B. $(1,7)$
• C. $(2,1)$
• D. $(2,5)$
• E. $(5,7)$

Answer 1

The correct option is A $(1,2)$

The intersection point of diagonals of rectangle is midpoint of each diagonal.

Let the fourth coordinate be $(x,y)$. By the above property we get

$\frac{x+5}{2}=\frac{1+5}{2}$. which implies $x=1$.

$\frac{y+5}{2}=\frac{2+5}{2}$. which implies $y=2$).

So, the coordinate $(x,y)$ is $(1,2)$.