Question

Show that A(1,2) B(4,3) C( 6,6) D(3,5) are the vertices of a parallelogram

Show that ABCD is not a rectangle​

Answer 1

Answer:

Given that,

A(1,2), B(4,3), C(6,6), D(3,5).

the distance between (x1,x2) and (y1,y2)=√(x2-x1)²+(y2-y1)²

Distance between A and B=√(4-1)²+(3-2)²

=√3²+1²=√9+1=√10 units

Distance between B and C=√(6-4)²+(6-3)²

=√2²+3²=√4+9=√12 units

Distance between C and D=√(3-6)²+(5-6)²

=√(-3)²+(-1)²=√9+1=√10 units

Distance between D and A=√(3-1)²+(5-2)²

=√2²+3²=√4+9=√12 units.

Distance between A and C=√(6-1)²+(6-2)²

=√5²+4²=√25+16=√41 units

Distance between B and D=√(3-4)²+(5-3)²

=√(-1)²+(2)²=√1+4=√5 units.

We notice that,

AB=CD, BC=DA and AC≠BD

therefore the vertices form a parallelogram.