The point P \[(3,4)\] is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (iii) the perimeter of the quadrilateral POP’O’.

Home » The point P is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (iii) the perimeter of the quadrilateral POP’O’.

The point P

$(3,4)$

is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (iii) the perimeter of the quadrilateral POP’O’.

The point P

$(3,4)$

is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (iii) the perimeter of the quadrilateral POP’O’.

According to the question:,

P’ is the image of P

$(3,4)$

reflected in x- axis and O’ is the image of O the origin in the line P’P.

(iii) Perimeter of POP’O’ is (

$4$

x OP) units.

Let Q be the point of intersection of diagonals OO’ and PP’.

So, OQ =

$3$

units and OP =

$4$

units

Hence,

$OP\text{ }=\text{ }\surd [{{\left( OQ \right)}^{2}}~+\text{ }{{\left( PQ \right)}^{2}}]\text{ }=\text{ }\surd \text{ }({{3}^{2}}~+\text{ }{{4}^{2}})\text{ }=\text{ }\surd \left( 9\text{ }+\text{ }16 \right)\text{ }=\text{ }\surd 25\text{ }=\text{ }5$

units

Thus, the perimeter of POP’O’ =

$4\text{ }\times \text{ }5\text{ }=\text{ }20$

units

i

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