An aquarium is a transparent tank of water in which live fish and other water creatures and plants are kept.
The diagram below shows the plans for an aquarium. It will be built in hexagonal shape. It will be made using
• Six rectangular shaped clear glasses
• One regular hexagon clear glass for roof.Refer to Top View
a) The value of x for which the distance between the points F(2 , − 3) and C( x, 5) is 10 , is
i) 8 or – 4 ii) 4 or 8 iii) 5 or – 10 iv) 5 or 10
b) The mid-point of the line segment joining the points E (8 ,11) and B ( 11, 15) is
i) ( 6, 10) ii) (
11
5
,
8
5
) iii)( 17 ,
15
4
) iv) (
19
2
, 13)
Refer to Front View
c) The distance of a point F( 8, 6) from origin is
i) 12 units ii) 16 units iii) 14 units iv)10 units
d) The perimeter of the square EFHI where E( − 2, 0) , F (3 , 0), H ( 3, 5) and I ( −2, 5) is
i) 8√5 units ii) 40 units iii) 20 units iv) none of these
e) The coordinates of the point which divides segment joining the point A( − 4, 5) and D (6 ,3) in
the ratio 3: 2 internally is
i) ( 0, 8) ii) (2,
19
5
) iii) ( 8,
13
2
) iv) (
7
5
, 3)
Answers
Question 1) :- The value of x for which the distance between the points F(2 , − 3) and C( x, 5) is 10 , is
i) 8 or – 4 ii) 4 or 8 iii) 5 or – 10 iv) 5 or 10
Solution :-
using Distance formula we get,
→ √[(x2 - x1)² + (y2 - y1)²] = FC
→ √[(x - 2)² + (5 - (-3))²] = 10
squaring both sides ,
→ (x - 2)² + 64 = 100
→ (x - 2)² = 100 - 64
→ (x - 2)² = 36
square - root both sides,
→ x - 2 = ±6
therefore,
→ x = (6 + 2) or (-6 + 2) = 8 or (-4) (option i) (Ans.)
Question 2) :- The mid-point of the line segment joining the points E (8 ,11) and B ( 11, 15) is ?
Solution :-
Let the coordinates of mid - points are x and y .
so,
→ x = (x1 + x2)/2 = (8 + 11)/2 = (19/2)
→ y = (y1 + y2)/2 = (11 + 15)/2 = 26/2 = 13 .
therefore, (19/2, 13) (option iv) (Ans.)
Question 3) :- The distance of a point F( 8, 6) from origin is
i) 12 units ii) 16 units iii) 14 units iv)10 units
Solution :-
we know that, coordinates of origin are (0,0) .
so, using distance formula we get,
→ Distance = √(8 - 0)² + (6 - 0)² = √(64 + 36) = √100 = 10 units. (option iv) (Ans.)
Answer:
whats the answer od d and e