Question

An aquarium is a transparent tank of water in which live fish and other water

creatures and plants are kept.

The diagrams 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 C x 2, 3 & ,5     is 10 is

(i) 8 or -4 (ii) 4 or 8 (iii) 5 or -10 (iv) 5 or 10

(b) The midpoint of the line segment joining the points E(8, 11) and B(11, 15) is

(i) (6, 10) (ii) 11 8

,

5 5

      (iii) 15 17,

4

      (iv) 19 ,13

2

     

Refer to Front view:

(c) The distance of the point F(7, 3) from the origin is

(i) 58 units (ii) 85 units (iii) 29 units (iv) 2 29 units

(d) The perimeter of a square EFHI where E(-2, 0), F(3, 0), H(3, 5) and I(-2, 5) is​

Answer 1

Answer:

1). (i) (8, -4)

2). (iv) (19/2, 13)

3). (iv) 10 units

4). (iii) 20 units

5). (ii) (2, 19/5)

Step-by-step explanation:

i). - $\sqrt{(2-x)^{2} +(-3-5)^2} \\\sqrt{4+x^2-4x+64}$= 10

      $68 + x^2 -4x = 100\\x^2-4x-32=0\\x^2 - 8x + 4x -32=0\\x(x-8) + 4(x-8)=0\\\\x=8 or x=-4$

2). - using section formula you can find the point coordinates

3). - origin (0,0) and the point you can use distance formula to find the answer

4). - find the distance of any one side, i took EF and multiplied it by 4

5). - using section formula you can find the coordinates of the point.