Question

Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was

having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 column
and 12 rows. The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot. He arranged the tile in such a way that colour of tiles in each row and column were in the pattern: Orange-> Yellow-> green->Blue Orange and so on.

Now answer the following questions:

i Which colour tile was fitted at the point with coordinates (5, 3)?

a. Orange

b. Yellow

c. Green

d. Blue

ii. Which colour tile was fitted at the point with coordinates (7.7)?

a. Orange

b. Yellow

c Green

d. Blue

iii. Which colour tile was fitted at the point with coordinate (2,5)?

a. Orange

b. Yellow

c. Green

d. Blue

iv. What is the area of the tiles fitted in the rectangular part OABX?

a. 50 foot2 b. 24 foot2

c. 12 foor2

d. 48 foot2

v. What is the ordinate of top row tiles?

a. 8.

b. 12

c. 16

d. 6​

Answer 1

Answer:

1 . (c) GREEN

2 . (b) Yellow

3 . (b) Yellow

4 . (d) 48 foot²

5 . (a) 8

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Answer 2

• The color of the tile that was fitted at the point with coordinates (5, 3) is equal to Green .
• The color of the tile that was fitted at the point with coordinates (7, 7) is equal to Orange .
• The color of the tile that was fitted at the point with coordinates (2, 5) is equal to Yellow .
• The area of the tiles fitted in the rectangular part OABX is equal to 48 foot² .
• The ordinate of top row tiles is equal to 12 .

Given :-

• Roshan decorated one of his bathroom wall with tiles as shown in the picture.
• He fitted the tiles in 8 column and 12 rows.
• The size of one tile was 1 foot x 1 foot and the area of each tile is 1 foot.
• He arranged the tile in such a way that colour of tiles in each row and column were in the pattern : Orange -> Yellow -> green -> Blue -> Orange and so on .

To Find :-

i) Which colour tile was fitted at the point with coordinates (5, 3) ?

ii) Which colour tile was fitted at the point with coordinates (7.7) ?

iii) Which colour tile was fitted at the point with coordinate (2,5) ?

iv) What is the area of the tiles fitted in the rectangular part OABX ?

v) What is the ordinate of top row tiles ?

Formula used :-

• According to distance formula, the distance between (a, b) and (c, d) = √[(c - a)² + (d - b)²]
• Area of rectangle = Length × Breadth .
• The perpendicular distance of the point from the x - axis is known as the ordinate .

Solution :-

from image we can see that,

→ The tile that was fitted at the point with coordinates (5, 3) = Green (c)

→ The tile that was fitted at the point with coordinates (7, 7) = Orange (a)

→ The tile that was fitted at the point with coordinates (2, 5) = Yellow (b)

now, in rectangle OABX we have,

• Coordinates of point O = (0,0)
• Coordinates of point A = (0, 6)
• Coordinates of point B = (8,6)
• Coordinates of point X = (8, 0)

So,

→ Distance between OA = √[(0 - 0)² + (6 - 0)²] = √(0² + 6²) = √(36) = 6 foot

→ Distance between OX = √[(8 - 0)² + (0 - 0)²] = √(8² + 0²) = √(64) = 8 foot

then,

→ Area of rectangular part OABX = Length × Breadth

→ Area of rectangular part OABX = OX × OA

→ Area of rectangular part OABX = 8 × 6

→ Area of rectangular part OABX = 48 foot² (d)

Now, from image we can see that,

• Coordinates of top rows tiles are :- (1,12), (2,12), (3,12) so on .

therefore,

→ The ordinate of top row tiles = 12 (b)

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