Question #cbcb6

Question

238 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-29T17:48:37

True

from the given coordinates,

#AB =sqrt((1-4)^2+(4-(-1))^2)# or, #sqrt 34#

#BC =sqrt((4-(-1))^2+(-1-(-4))^2)# or, #sqrt 34#

#CD =sqrt((-1-(-4))^2+(-4-1)^2)# or, #sqrt34#

#DA =sqrt((-4-1)^2+(1-4)^2)# or, #sqrt 34#

So,all the sides of the polygon has the same length,so the diagonals will bisect each other.

Now, Diagonal #AC =sqrt((1-(-1))^2+(4-(-4))^2)# or, #sqrt68#

and, #BD =sqrt((4-(-4))^2+(-1-1)^2)# or, #sqrt68#

ALTERNATIVELY,

Now, equation of the staright line # BD# is #(y-(-1))/(x-4)=(y-1)/(x-(-4))# or, #x=-4y#

Now, mid point of #AC# is #((1+(-1))/2),((4+(-4))/2)# i.e #(0,0)#

Clearly, #(0,0)# is also a point on #BD#,i.e #BD# will pass through #(0,0)#,so they will bisect each other.