*Case Study : 1×4=4 In an examination hall ,students are seated at a distance ofONA virus pandemic .Let three students sit at a points A, B and C whose coordinates are (4, - 3) ,(7,3) and (8,5) resp. Based on the above information, answer the following questions. (i) The distance between A and C is (a) √5units (b) 4√5units (c) 3√5units (b) None of these (ii) If an invigilator at the point I , lying on the straight line Joining B and C such that it divides the distance Between them in the ratio 1: 2 .Then coordinates of I are (a) (22/3,11/3) (b) (23/3,13/3) (b) (6,1) (d) (9,1) iii) The ratio in which B divides the line segment joining A and C is (a) 2:1 (b) 3:1 (c) 1:2 (d) none of these iv) The mid-point of the line segment joining A and C is (a) (1,6) (b) (6,2) (c) (11/2,0) (d) none of these
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Answer:
According to the fig. A(3,4),B(6,7),C(9,4) and D(6,1) are the position of 4 friends .
If we join all these points then
By using distance formula
=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
AB=
(3−6)
2
+(4−7)
2
=
(−3)
2
+(−3)
2
=
9+9
=
18
=3
2
BC=
(6−9)
2
+(7−4)
2
=
(−3)
2
+(3)
2
=
9+9
=
18
=3
2
CB=
(9−6)
2
+(4−1)
2
=
(3)
2
+(3
2
)
=
9+9
=
18
=3
2
AD=
(3−6)
3
+(4−1)
2
=
−3)
2
+(3)
2
=
9+9
=
18
=3
2
if we join the point AC and BD than
DiagonalAC=
(3−9)
2
+(4−4)
2
=
(−6)
2
+(0)
2
=
36
=6
Diagonal BD=
(6−6)
2
+(7−1)
2
=
(0)
2
+(6)
2
=
36
=6
Hence all the sides of a quadrilateral are the same and the diagonals are also the same so ABCD is a square.
Hence Champa is correct.
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