# Q.31. Children of a school planned to plant trees in their school. They planted tree in a pattern. Plot the following coordinates; A (- 2, 2), B (- 2, - 2), C (4, - 2) and D (4, 2). Join the points in order. What is the figure you get? Which values of the children depicted here?

Dear Student,

We plot given coordinates on a graph , As :

We know : Distance formula :  d =

Then, to find Length of AD , We get x1 = - 2  , y1 = 2  and  x2 = 4  , y2 = 2

And to find Length of BC , We get x1 = - 2  , y1 = - 2  and  x2 = 4  , y2 = - 2

BC  = = 6 unit

So,

AD  =  BC                                                     --- ( 1 )

And we know equation of line when two coordinates on the line is given : ( y - y1 ) = ( x - x1
Then, to find equation of line AD , We get x1 = - 2  , y1 = 2  and  x2 = 4  , y2 = 2

So, AD is parallel to ' x - axis '  .                                  --- ( 2 )

And to find equation of line BC , We get x1 = - 2  , y1 = - 2  and  x2 = 4  , y2 = - 2

Equation of BC :

So, BC is parallel to ' x - axis '  .                                  --- ( 3 )

From statements ( 2 ) and ( 3 )  we get   AD | | BC  | | x - axis                           --- ( 4 )

Similarly we can show : AB | | CD  | | y - axis

And we know x - axis and y axis are perpendiculars to each other , So

AD $\perp$ AB and AD $\perp$ CD  , BC $\perp$ AB and BC $\perp$ CD                                   --- ( 5 )

From equation , 1 4 and 5 we get  :

ABCD is a rectangle .

And by doing this work students depicted their caring nature towards environment .