Question

Plot the points (0,0), (4,0),(4,3) and (0,3) and show that they form a rectangle.

Answer 1

$\huge\mathfrak{Hola\: Mate}$

$\huge{Solution:-}$

$refer \: the \: figure \: shown \: in \: image,$

$let \: the \: vertices \: of \: quadriateral \: \: be = \\ a(0 \:, \: 3) \\ b(4 \: , \: 3) \\ c(0 \: , \: 0) \\ d(4 \: , \: 0)$

$distance \: formula = \sqrt{ {(x - x1)}^{2} + {(y - y1)}^{2} }$

$in \: rectangle \: opposite \: sides \: are \: equal \\ therefore \: , \: ab = cd$

$by \: using \: distance \: formula = \\ \sqrt{( {0 - 4)}^{2} + {(3 - 3)}^{2} } = \sqrt{ {(0 - 4)}^{2} + {(0 - 0)}^{2} }$

$\sqrt{ { (- 4)}^{2} } = \sqrt{( {4)}^{2} }$

$\sqrt{16} = \sqrt{16}$

$4 = 4$

$similarly \: , \: ac = bd$

$hence \: is \: is \: poved \: that \: quadrilateral \: is \: rectangle \: beacause \: its \: opposide \: sides \: are \: equal$

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Answer 2

Step-by-step explanation:

\huge\mathfrak{Hola\: Mate}HolaMate

\huge{Solution:-}Solution:−

refer \: the \: figure \: shown \: in \: image,referthefigureshowninimage,

\begin{lgathered}let \: the \: vertices \: of \: quadriateral \: \: be = \\ a(0 \:, \: 3) \\ b(4 \: , \: 3) \\ c(0 \: , \: 0) \\ d(4 \: , \: 0)\end{lgathered}

lettheverticesofquadriateralbe=

a(0,3)

b(4,3)

c(0,0)

d(4,0)

distance \: formula = \sqrt{ {(x - x1)}^{2} + {(y - y1)}^{2} }distanceformula=

(x−x1)

2

+(y−y1)

2

\begin{lgathered}in \: rectangle \: opposite \: sides \: are \: equal \\ therefore \: , \: ab = cd\end{lgathered}

inrectangleoppositesidesareequal

therefore,ab=cd

\begin{lgathered}by \: using \: distance \: formula = \\ \sqrt{( {0 - 4)}^{2} + {(3 - 3)}^{2} } = \sqrt{ {(0 - 4)}^{2} + {(0 - 0)}^{2} }\end{lgathered}

byusingdistanceformula=

(0−4)

2

+(3−3)

2

=

(0−4)

2

+(0−0)

2

\sqrt{ { (- 4)}^{2} } = \sqrt{( {4)}^{2} }

(−4)

2

=

(4)

2

\sqrt{16} = \sqrt{16}

16

=

16

4 = 44=4

similarly \: , \: ac = bdsimilarly,ac=bd

hence \: is \: is \: poved \: that \: quadrilateral \: is \: rectangle \: beacause \: its \: opposide \: sides \: are \: equalhenceisispovedthatquadrilateralisrectanglebeacauseitsopposidesidesareequal

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