c 1 20. Show that: (i) the points (0, -2), (3, 1), (0, 4), (-3, 1) are the vertices of a square. (ii) the points (0, -1) (-2, 3), (6, 7), (8, 3) are the vertices of a rectangle.
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Answer:
Hence proved.
Step-by-step explanation:
(i)
let A(0,-2),B(3,1),C(0,4),D(-3,1)
to prove the given vertex is a square all the lengths or the distance b/w vertex should be equal on all sides so
distance AB=√[(x2-x1)²+(y2-y1)²]
=√[(3-0)²+(1-(-2))²]
=√18
=2√9
similarly for BC,CD,DA if all the values equal then it is a square.
(ii)
P(0,-1),Q(-2,3),R(6,7),S(8,3)
to prove the given vertex is a rectangle opposite sides should be equal
like , distance between PQ=RS,PS=QR
distance PQ=√[(x2-x1)²+(y2-y1)²]
=√[(-2-0)²+(3-(-1))²]
=√20
=2√5
similarly, RS =2√5
distance PS=√[(x2-x1)²+(y2-y1)²]
=√[(8-0)²+(-1-3)²]
=√80
=4√5
similarly, QR=4√5
So, PQ = RS and PS = QR
Therefore, PQRS is a rectangle.
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