Question

Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).

• A. (4,-2)
• B. (-4,2)
• C. (-4,-2)
• D. (-4,0)

Answer 1

Answer: (A), (B), (C)

(-4,-2)

From the data given the rectangle formed is shown below.

Let B =(4,2)

Let the points where rectangle cuts X-axis be x and $x^1$. and the points where it cuts Y-axis is y and $y^1$.

Now $X{X}^1=AB=CD$.

and O is midpoint of $X{X}^1$.

$\Rightarrow OX=O{X}^1$

$\therefore X^1=(-4,0)$

$\therefore A=(-4,2)$

Now $Y{Y}^1=BC=AD$

Now BX =OY =2

$\therefore O{Y}^1=2(\because OY=O{Y}^1)$

$\Rightarrow XC=2\&X^{1}D=2$

$\therefore C=(4,-2)\&D=(-4,-2)$