Math, asked by Anonymous, 8 months ago

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Answered by MoodyCloud

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Question:-

Name the type of quadrilateral formed , if any , by the following points , and give reasons for you answer

(-1,-2),(1,0),(-1,2),(-3,0)
(-3,5),(3,1),(0,3),(-1,-4)
(4,5),(7,6),(4,3),(1,2)

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Answer:-

(i) (-1,-2),(1,0),(-1,2),(-3,0)

Ans.

(-1,-2) A

(1,0) B

(-1,2) C. { Take this all as A, B , C and D}

(-3,0) D

➢ AB =

$\sqrt{ {( - 1 - 1)}^{2} + {( - 2)}^{2} } = \sqrt{4 + 4} = 2 \sqrt{2}$

➢BC

$\sqrt{ {(1 + 1)}^{2} + {(0 - 2)}^{2} } = \sqrt{4 + 4 } = 2 \sqrt{2}$

➢ CD

$\sqrt{ {( - 1 + 3)}^{2} + {(2 - 0)}^{2} } = \sqrt{4 + 4} = 2 \sqrt{2}$

➢DA

$\sqrt{ {( - 3 - 1)}^{2} + {(0 + 2)}^{2} } = \sqrt{4 + 4} = 2 \sqrt{2}$

➢ Ac

$\sqrt{ {( -1- 1)}^{2} + {(-2- 2)}^{2} } = \sqrt{0+16} = 4$

➢ Bd

$\sqrt{ {( 1+3)}^{2} + {(0 + 0)}^{2} } = \sqrt{16+0} = 4$

All four sides are equal and diagonal are also equal . So, it is a square.

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(ii) (4,5),(7,6),(4,3),(1,2)

(4,5) A

(7,6) B

(4,3) C. {Take this all like A ,B, C and D}

(1,2) D

➢ AB =

$\sqrt{ {( -3-3)}^{2} + {( 5-1)}^{2} } = \sqrt{36+16} = \sqrt{52} = 2\sqrt{3}$

➢BC

$\sqrt{ {(3-0)}^{2} + {(1-3)}^{2} } = \sqrt{9+14 } = \sqrt{13}$

➢ CD

$\sqrt{ {( 0+1)}^{2} + {(3+4)}^{2} } = \sqrt{1+49} = \sqrt{50} =5\sqrt{2}$

➢DA

$\sqrt{ {( -1+3)}^{2} + {(-4-5)}^{2} } = \sqrt{4 + 81} = \sqrt{85}$

All four sides are not equal so it is not a specific quadrilateral.

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(iii)(4,5),(7,6),(4,3),(1,2)

(4,5) A

(7,6) B

(4,3) C. {Take this all like A ,B, C and D}

(1,2) D

➢ AB =

$\sqrt{ {(4-7)}^{2} + {( 5-6)}^{2} } = \sqrt{{( 3)}^{2}+{( -1)}^{2}} = \sqrt{9+1}= \sqrt{10}$

➢BC

$\sqrt{ {(7-4)}^{2} + {(6-3)}^{2} } = \sqrt{ {( 3)}^{2}+{( 3)}^{2}} = \sqrt{9+9} =\sqrt{18}$

➢ CD

$\sqrt{ {( 4-1 )}^{2} + {(3-2)}^{2} } = \sqrt{{( 3)}^{2}+{( 1)}^{2}} = \sqrt{9+1}=\sqrt{10}$

➢DA

$\sqrt{ {( 4-1)}^{2} + {(5-2)}^{2} } = \sqrt{{( 3)}^{2}+{( 3)}^{2}} = \sqrt{9+9} =\sqrt{18}$

➢ Ac

$\sqrt{ {( 4-4)}^{2} + {(5-3)}^{2} } = \sqrt{{( 0)}^{2}+{( 2)}^{2}} = \sqrt{0+4}=2$

➢ CD

$\sqrt{ {( 7-1)}^{2} + {(0-2)}^{2} } = \sqrt{{( 6)}^{2}+{( 4)}^{2}} = \sqrt{36+6}= \sqrt{52} = 13 \sqrt{2}$

All four sides are not equal but two pairs of opposite sides are equal and diagonal are not equal.This a quadrilateral rhe given point sa re vertices of parallelogram.

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BrainlyRaaz: Perfect ✔️

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Question:-

_________________________

Answer:-

(i) (-1,-2),(1,0),(-1,2),(-3,0)

All four sides are equal and diagonal are also equal . So, it is a square.

(ii) (4,5),(7,6),(4,3),(1,2)

All four sides are not equal so it is not a specific quadrilateral.

(iii)(4,5),(7,6),(4,3),(1,2)

All four sides are not equal but two pairs of opposite sides are equal and diagonal are not equal.This a quadrilateral rhe given point sa re vertices of parallelogram.

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