Question

In green park New Delhi, Ramesh is having a rectangular plot ABCD. Saplings of gulmohar are planted on boundary at a distance of 1m. Ramesh builds his home in rectangular's area PQRS. Consider 'O' as the origin to answer the following questions. [¡]The co-ordinates of the vertices of P and S of a rectangle PQRS are i)(2,4)(6,4) ii)(4,2)(4,6) iii)(6,4)(2,4) iv)(4,6),(4,2.5) +47. The co-ordinates of midpoint of the diagonal QS is given by 17 )(7,4) ii) (6,2) iii)(7,4.25) iv)(13/2,4) 48. The area of house is iy18sq.m ii)28sq.m iii)12sq.m iv) 21sq.m 9. The co-ordinates of the vertices R and Q of PQRS are i)(10,6)(10,2) ii)(3,10)(10,6) i¡i)(10,2.5)(10,6) iv)(3,10)(6,1) 50. If 'S' is taken as the origin, then the co-ordinates of 'Q' are - i)(6,3.5) ii)(2,6) ii)(6,6) iv)(2,2) A.​

Answer 1

Answer:

In green park New Delhi, Ramesh is having a rectangular plot ABCD. Saplings of gulmohar are planted on boundary at a distance of 1m. Ramesh builds his home in rectangular's area PQRS. Consider 'O' as the origin to answer the following questions. [¡]The co-ordinates of the vertices of P and S of a rectangle PQRS are i)(2,4)(6,4) ii)(4,2)(4,6) iii)(6,4)(2,4) iv)(4,6),(4,2.5) +47. The co-ordinates of midpoint of the diagonal QS is given by 17 )(7,4) ii) (6,2) iii)(7,4.25) iv)(13/2,4) 48. The area of house is iy18sq.m ii)28sq.m iii)12sq.m iv) 21sq.m 9. The co-ordinates of the vertices R and Q of PQRS are i)(10,6)(10,2) ii)(3,10)(10,6) i¡i)(10,2.5)(10,6) iv)(3,10)(6,1) 50. If 'S' is taken as the origin, then the co-ordinates of 'Q' are - i)(6,3.5) ii)(2,6) ii)(6,6) iv)(2,2) A.

Answer 2

Given: In green park New Delhi, Ramesh is having a rectangular plot ABCD. Saplings of gulmohar are planted on boundary at a distance of 1m. Ramesh builds his home in rectangular's area PQRS. Consider 'O' as the origin.

To find:

[¡] The co-ordinates of the vertices of P and S of a rectangle PQRS.

[ii] The co-ordinates of midpoint of the diagonal QS.

[iii] The area of house.

[iv] The co-ordinates of the vertices R and Q of PQRS .

[v] If 'S' is taken as the origin, then the co-ordinates of 'Q'.

Solution:

In the given figure, the side OD of the rectangle is considered to be the x-axis and the sides OB of the rectangle is considered to be the y-axis.

[i]

So, the co-ordinates of the vertex of P is (4,6) and the co-ordinates of the vertex of S is (4,2.5).

[ii]

The x-coordinates of the midpoint of the diagonal QS is

$\frac{(10-4)}{2} = 3$

$4+3 = 7$

And the y-coordinates of the midpoint of the diagonal QS is

$\frac{(6-2.5)}{2} = 1.75$

$2.5 + 1.75 = 4.25$

So, the co-ordinates of the midpoint of the diagonal QS is (7,4.25).

[iii]

The length of the house is

$10 - 4 = 6$

The width of the house is

$6-2.5 = 3.5$

Thus, the area of the house is

$6*3.5 = 21$

[iv]

The co-ordinates of the vertex of R is (10,2.5) and the co-ordinates of the vertex of Q is (10,2.5).

[v]

The x-coordinates of point Q is

$10-4 = 6$

And the y-coordinates of point Q is

$6 - 2.5 = 3.5$

So, the co-ordinates of point Q is (6,3.5).

Therefore,

[i] The co-ordinates of the vertices of P and S of a rectangle PQRS is (4,2.5).

[ii] The co-ordinates of midpoint of the diagonal QS is (7,4.25).

[iii] The area of house is 21 sq. m.

[iv] The co-ordinates of the vertices R and Q of PQRS is (10,2.5).

[v] If 'S' is taken as the origin, then the co-ordinates of 'Q' is (6,3.5).