Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) $(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)$
(ii) $(- 3, 5), (3, 1), (0, 3), (- 1, - 4)$
(iii) $(4, 5), (7, 6), (4, 3), (1, 2)$

Question

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i)

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

(ii)

(- 3, 5), (3, 1), (0, 3), (- 1, - 4)

(iii)

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

Filo · Accepted Answer

(i) Let the given points are A(−1,−2), B(1,0), C(−1,2)and D(−3,0) Then,AB=(1+1)2+(0+2)2​=22+22​=4+4​=8​BC=(−1−1)2+(2−0)2​=(22+22)​=4+4​=8​CD=((−3)−(−1))2+(0−2)2​=22+(−2)2​=4+4​=8​DA=(−3)−(−1))2+(0−(−2))2​=(−2)2+22​=4+4​=8​AC((−1)−(−1))2+(2−(−2))2​=0+42​=16​=4BD=(−3−1)2+(0−0)2​=−42​=16​=4Since the four sides AB,BC,CD and DA are equal  and the diagonals AC and BD are equal .∴ Quadrilateral  ABCD is a square.(ii)Let the given points are A(−3,5),B(3,1),C(0,3) and D(−1,−4)ThenAB=(−3−3)2+(5−1)2​=(−6)2+42​=36+16​=52​BC=(3−0)2+(1−3)2​=(32+(−2)22)​=9+4​=11​CD=(0−(−1))2+(3−(−4))2​=12+(7)2​=1+49​=50​DA=(−1)−(−3))2+((−4)−5))2​=(2)2+(−9)2​=4+81​=85​Here AB=BC=CD=DA∴ it is a quadrilateral.(iii)Let the given points are A(4,5),B(7,6),C(4,3) and D(1,2)ThenAB=(7−4)2+(6−5)2​=32+12​=9+1​=10​BC=(4−7)2+(3−6)2​=((−3)2+(−3)2)​=9+9​=18​CD=(1−4)2+(2−3)2​=(−3)2+(−1)2​=9+1​=10​DA=(1−4)2+(2−5)2​=(−3)2+(−3)2​=9+9​=18​AC(4−4)2+(3−5)2​=0+(−2)2​=4​=2BD=(1−7)2+(2−6)2​=(−6)2+(−4)2​=36+16​=52​Here AB=CD,BC=DA . But AC=BDHence the pairs of opposite sides are equal but diagonal are not equal so it is a parallelogram.

Question Text	Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) $(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)$ (ii) $(- 3, 5), (3, 1), (0, 3), (- 1, - 4)$ (iii) $(4, 5), (7, 6), (4, 3), (1, 2)$
Answer Type	Text solution:1
Upvotes	151

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) $(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)$
(ii) $(- 3, 5), (3, 1), (0, 3), (- 1, - 4)$
(iii) $(4, 5), (7, 6), (4, 3), (1, 2)$

Text solutionVerified

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Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:(i) (−1,−2),(1,0),(−1,2),(−3,0)(ii) (−3,5),(3,1),(0,3),(−1,−4)(iii) (4,5),(7,6),(4,3),(1,2)

Text solutionVerified

Practice questions from similar books

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) $(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)$
(ii) $(- 3, 5), (3, 1), (0, 3), (- 1, - 4)$
(iii) $(4, 5), (7, 6), (4, 3), (1, 2)$