A playground is marked with 10 10 grid as shown in fig. Three parrots are sitting at
points P, (3, 4).P,(6, 7).P,9,4) respectively. A koel'K'joins them and sit somewhere
in the triangular region described by AP PP,
10
192
2
10
Consider O as origin, answer questions (i) to (v).
Ifkoel sit exactly on mid-point of P,P, what are its coordinates ?
(a) G
(b) (6,4)
(c) (3)
(d) (6,5)
(11)
Ifkoel sits at centroid of AP,P.P.The following point best describes its location.
(a) (6,5)
(b) (6,4)
(c) (3,9)
(iii) Distance of koel 'K' from P, in position (i) mentioned above is given by
(a) 9 units
(b) 6 units
(c) 3 units
(d) 12 units
(iv) Distance ofkoel 'K' from P, in position (ii) mentioned above is given by
(a) 3 units
(b) 1 unit
(c) 2 units
(d) 5 units
(v) Ifkoel sits at a point which is equidistant from all three parrots, then position of
koel is actually
(a) In centre of A
(b) circum centre of A
(c) Centroid of D
(d) orthocenter of
Answers
Given : Three parrots are sitting at points P₁ (3, 4), P₂(6, 7), P₃(9,4)
To Find : If koel sit exactly on mid-point of P₁ (3, 4), P₃(9,4)
what are its coordinates
If koel sit at centroid of ΔP₁P₂P₃
what are its coordinates
Solution:
P₁ (3, 4), P₃(9,4)
koel sit exactly on mid-point of P₁ (3, 4), P₃(9,4)
coordinates = ( 3 + 9)/2 , (4 + 4)/2
= 6 , 4
koel sit at centroid of ΔP₁P₂P₃
P₁ (3, 4), P₂(6, 7), P₃(9,4)
centroid = ( 3 + 6 + 9)/3 , ( 4 + 7 + 4)/3
= 6 , 5
Distance of P₁ (3, 4) from (6 ,4 )
= √(6- 3)² + (4 - 4)²
= √3² + 0
= 3 unit
Distance of P₂(6, 7) from (6 ,4 )
= √(6- 6)² + (6 - 4)²
= √0+3²
= 3 unit
Circumcenter of triangle is at Equal distance from all vertex
Learn More:
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Answer :-
P₁ (3, 4), P₃(9,4)
koel sit exactly on mid-point of P₁ (3, 4), P₃(9,4)
coordinates = ( 3 + 9)/2 , (4 + 4)/2
= 6 , 4
koel sit at centroid of ΔP₁P₂P₃
P₁ (3, 4), P₂(6, 7), P₃(9,4)
centroid = ( 3 + 6 + 9)/3 , ( 4 + 7 + 4)/3
= 6 , 5
Distance of P₁ (3, 4) from (6 ,4 )
= √(6- 3)² + (4 - 4)²
= √3² + 0
= 3 unit
Distance of P₂(6, 7) from (6 ,4 )
= √(6- 6)² + (6 - 4)²
= √0+3²
= 3 unit
Circumcenter of triangle is at Equal distance from all vertex