Question

If $A(4,1),B(7,4),C(13,-2)$ are the three consecutive vertices of a rectangle $ABCD$, then the coordinates of $D$ are

• A. $(10,5)$
• B. $(-10,5)$
• C. $(10,-5)$
• D. $(-10,-5)$

Answer 1

The correct option is C $(10,-5)$

Let $D(x,y)$ be the fourth vertex.
We know that diagonals of a rectangle bisect each other.

Mid point of $BD=$ Mid point of $AC$
$\Rightarrow (\frac{x+7}{2},\frac{y+4}{2})=(\frac{4+13}{2},\frac{1-2}{2})\Rightarrow x=10,y=-5\therefore D=(10,-5)$