A(1, 2), B(2, 3), C(3, 4) are given points. ...... of the following is true.select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) AC+BC=AB
(b) AB+BC=AC
(c) A is the mid-point of BC
(d) A,B,C are non-collinear.
Answers
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5
(b) AB +BC=AC is the right answer
Answered by
13
Given A( 1,2 ) , B( 2 , 3 ) , C( 3,4 )
are three points ,
By distance formula :
i ) AB = √(x2 - x1)² + ( y2 - y1 )²
= √ ( 2 - 1 )² + ( 3 - 2 )²
= √ 1 + 1
AB = √2 ----( 1 )
ii ) B( 2 , 3 ), C( 3, 4 )
BC = √( 3 - 2 )² + ( 4 - 3 )²
= √ 1 + 1
= √2
BC = √2 ---( 2 )
iii ) C( 3 , 4 ) , A( 1 , 2 )
CA = √( 1 - 3 )² + ( 2 - 4 )²
= √ ( - 2 )² + ( -2 )²
= √ 4 + 4
= √ 8
CA = 2√2----( 3 )
From ( 1 ) , (2 ) and ( 3 ) , we get
AB + BC = AC
Option ( b ) is correct.
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