Question

The point P(5, 3) was reflected in the origin to get P'. If M is foot of the perpendicular from P to x -axis & N is foot of the perpendicular from P' to x -axis , Name the figure PMP'N

• A. Rectangle
• B. Paralleogram
• C. Rhombus
• D. Square

Answer 1

The correct option is B

Paralleogram

P' is image after reflection of point P(5, 3) of point P (-5, -3)

$PM=\sqrt{(5-5{)}^2+(3-0{)}^2}=3$

$P^{\prime }N=\sqrt{(-5-(-5){)}^2+(-3,-0{)}^2}=3$

$PN=\sqrt{{[5-(-5\left)\right]}^2+(3-0{)}^2}=\sqrt{100+9}=\sqrt{109}$

$P^{\prime }M=\sqrt{(-5-5{)}^2+(-3-0{)}^2}=\sqrt{100+9}=\sqrt{109}$

Opposite sides are equal and parallel - Hence it is a parallelogram.