5. In a classroom, 4 friends are
seated at the points A, B, C and
Das shown in Fig. 7.8. Champa
and Chameli walk into the class
and after observing for a few
minutes Champa asks Chameli,
"Don't you think ABCD is a
square?" Chameli disagrees.
Using distance formula, find
which of them is correct.
Answers
Solution :
Given points are A(3,4), B(6,7),
C(9,4) and D(6,1)
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Distance between (x1,y1) , ( x2 ,y2 )
= √ ( x2 - x1 )² + ( y2 - y1 )²
*****************************************
i ) Distance between A and B
= √ ( 6 - 3 )² + ( 7 - 4 )²
= √ 3² + 3²
= √ 9 + 9
AB = √18
ii ) Distance between B and C
= √ ( 9 - 6 )² + ( 4 - 7 )²
= √ 3² + 3²
= √ 9 + 9
BC = √18
iii ) Distance between C And D
= √ ( 6 - 9 )² + ( 1 - 4 )²
= √ 9 + 9
BC = √18
iv ) Distance between D and A
= √( 3 - 6 )² + ( 4 - 1 )²
= √ 9 + 9
DA = √18
v ) Distance between A and C
= √ ( 9 - 3 )² + ( 4 - 4 )²
= √ 36
AC = 6 units
vi ) Distance between B and D
= √ ( 6 - 6 )² + ( 1 - 7 )²
= √ 36
BD = 6 units
Therefore ,
AB = BC = CD = DA
and
AC = BD
Jarina's answer is correct
ABCD becomes a Square.
hope it helps
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