Question

Karan went to the Lab near to his home for COVID 19 test along with his family

members. The seats in the waiting area were as per the norms of distancing during this

pandemic (as shown in the above figure). His family member took their seats

surrounded by red circular area.

(i) Considering A as the origin, what are the coordinates of A?

a) (0,1) b) (1,0) c) (0,0) d)(-1,-1)

(ii) What is the distance between Neena and Karan ?

a) 10 b) 2√5 c)√10 d)√8

(iii) What are the coordinates of seat of Akash ?

a) (2,3) b) (3,2) c) (0,3) d) (2,0)

(iv) What will be the coordinates of a point exactly between Akash and Binu where a

person can be seated?

a) (3.5,2.5) b) (2.5,5) c) (10,5) d) (1.5,0.5)

(v) Determine the shape of the figure we get on joining the points where Karan’s family

members are seated.

a) Rectangle b ) Square c) Parallelogram d) Rhombus

please tell me fast​

Answer 1

1. The coordinate of A will be (0,0).

• In cartesian coordinates, the coordinates of the origin will be always equal to zero.
• In two dimensions, it will be (0,0) as well as in three dimensions it will be (0,0,0).
• Here, the cartesian is in two dimensions, hence the coordinates of origin will be (0,0).

2. The distance between Neena and Karan will be equal to $\sqrt{10}$ units.

Given:

The coordinates of Neena = (3,6)

The coordinates of Kiran = (6,5)

To Find:

The distance between Neena and Karan

Solution:

The distance between two coordinates can be found by,

$Distance = \sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1} ) ^{2} }$

Were,

$x_{1}$ = 3

$y_{1}$ = 6

$x_{2}$ = 6

$y_{2}$ = 5

By substituting the known values,

$Distance = \sqrt{(6 - 3) ^{2} + (5 - 6) ^{2} }$

Distance = $\sqrt{10}$ units

Hence, the distance between Neena and Karan will be $\sqrt{10}$ units.

3. The coordinates of the seat of Akash will be (2,3).

• Coordinates of a two-dimensional cartesian are represented as (x,y).
• Where, x is the unit on the x-axis similarly, y is the unit on the y-axis.
• According to this, the coordinates of Akash will be (2,3).

4. The coordinate of the point exactly between Akash and Binu will be

   (3.5,2.5).

Given:

The coordinates of Akash = (2,3)

The coordinates of Bine = (5,2)

To Find:

The coordinate of the point is exactly between Akash and Binu.

Solution:

The coordinate of the point exactly between Akash and Binu will be the midpoint of these coordinates.

According to the midpoint formula,

$(x_{m}, y_{m}) = (\frac{x_{1} + x_{2} }{2}) , (\frac{y_{1} + y_{2} }{2})$

Were,

$x_{1}$ = 2

$y_{1}$ = 3

$x_{2}$ = 5

$y_{2}$ = 2

By substituting the given values,

Coordinates = $(\frac{2 + 5 }{2}) , (\frac{3 + 2 }{2})$

Hence, the coordinate of the point exactly between Akash and Binu will be (3.5,2.5).

5. The rhombus will be the shape of the figure.

Given:

The coordinates of Akash = (2,3)

The coordinates of Neena = (3,6)

The coordinates of Karan = (6,5)

The coordinates of Binu = (5,2)

To Find:

The shape of the figure when we joint the points where Karan’s family members are seated.

Solution:

It's fairly simple to find the answer to this question, as seen below.

According to the distance formula,

$Distance = \sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1} ) ^{2} }$

By substituting the given values,

The Distance between Akash and Neena,

$Distance = \sqrt{(3-2) ^{2} + (6-3) ^{2} }$ $= \sqrt{10}$ units

Similarly,

The Distance between Neena and Karan = $\sqrt{10}$ units

The Distance between Karan and Binu = $\sqrt{10}$ units

The Distance between Binu and Akash = $\sqrt{10}$ units

When we join the points, all four sides of the figure are equal and parallel, and the opposite angles will be also equal.

Hence, the figure is rhombus.

#SPJ3

Answer 2

1. The coordinate of A will be (0,0).

   In cartesian coordinates, the coordinates of the origin will be always equal to zero.

   In two dimensions, it will be (0,0) as well as in three dimensions it will be (0,0,0).

   Here, the cartesian is in two dimensions, hence the coordinates of origin will be (0,0).

2. The distance between Neena and Karan will be equal to units.

Given:

The coordinates of Neena = (3,6)

The coordinates of Kiran = (6,5)

To Find:

The distance between Neena and Karan

Solution:

The distance between two coordinates can be found by,

Were,

= 3

= 6

= 6

= 5

By substituting the known values,

Distance = units

Hence, the distance between Neena and Karan will be units.

3. The coordinates of the seat of Akash will be (2,3).

   Coordinates of a two-dimensional cartesian are represented as (x,y).

   Where, x is the unit on the x-axis similarly, y is the unit on the y-axis.

   According to this, the coordinates of Akash will be (2,3).

4. The coordinate of the point exactly between Akash and Binu will be

  (3.5,2.5).

Given:

The coordinates of Akash = (2,3)

The coordinates of Bine = (5,2)

To Find:

The coordinate of the point is exactly between Akash and Binu.

Solution:

The coordinate of the point exactly between Akash and Binu will be the midpoint of these coordinates.

According to the midpoint formula,

Were,

= 2

= 3

= 5

= 2

By substituting the given values,

Coordinates =

Hence, the coordinate of the point exactly between Akash and Binu will be (3.5,2.5).

5. The rhombus will be the shape of the figure.

Given:

The coordinates of Akash = (2,3)

The coordinates of Neena = (3,6)

The coordinates of Karan = (6,5)

The coordinates of Binu = (5,2)

To Find:

The shape of the figure when we joint the points where Karan’s family members are seated.

Solution:

It's fairly simple to find the answer to this question, as seen below.

According to the distance formula,

By substituting the given values,

The Distance between Akash and Neena,

units

Similarly,

The Distance between Neena and Karan = units

The Distance between Karan and Binu = units

The Distance between Binu and Akash = units

When we join the points, all four sides of the figure are equal and parallel, and the opposite angles will be also equal.

Hence, the figure is rhombus.Answer

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