Question

show that A(-4,-7) B(-1,2) C(8,5) & D (5,-4)are the vertices of parallelogram,in slope​

Answer 1

to show that it is the vertices of a parallelogram we have to show that side AB is parallel to side CD ok so we have to show first this:

to show that the side AB is parallel to side CD we have to show that their slopes are equal that means that the slope of side AB should be equal to side CD

slope of AB

=-7-2/-4+1

=-9/-3

=3

slope of CD

=5+4/8-5

=9/3

=3

so as the Slope of AB is equal to that of slope of CD

so AB is parallel to CD ..

again to show that it is a parallelogram we have to show that the midpoint of BD is equal to the midpoint of AC so let's show it :

midpoint of BD :

=(- 1 + 5 , 2 - 4 )

=(4,-2)

midpoint of AC :

=(-4+8 , -7+5 )

=(4,-2)

so as the midpoint of BD is equal to the midpoint of AC and as AB is parallel to to CD so ABCD is a parallelogram..

Thank you..