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.$\left[4Marks\right]$

Answer 1

We know when any point (x, y) is reflected in the origin, the sign of its abscissa and ordinate both changes.

As, P' is the image of point P(5, 3) after reflection in the origin, therefore cooordinates of P' are (-5, -3).$\left[0.5Mark\right]$

$\left[1Mark\right]$

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

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

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

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

Opposite sides are equal and parallel, hence it is a parallelogram.$\left[0.5Mark\right]$