Answer:
Step-by-step explanation:
To prove this we should first make a little representation to get an idea of how will proceed to work .
To solve it we should use vectors so the first step is to identify this vectors :
- we have four points : A/B/C/D
- A(-2,-4)
- B(1,2)
- C(2,10)
- D(-1,4)
- VECTOR AB WITH VECTOR DC
- VECTOR AD WITH VECTOR BC
NOW LET'S IDENTIFY THEIR COORDINATES :
- VECTOR AB (1-(-2),2-(-4)) VECTOR DC (2-(-1),10-4)
- VECTOR AD (-1-(-2),4-(-4)) VECTOR BC (2-1,10-2)
We get :
- VECTOR AB (3,6) VECTOR DC (3,6)
- VECTOR AD (1,8) VECTOR BC (1,8)
We notice that the opposite ones have the same coordinates so the edges are parallel .
If we want to check more we can calculate the lenghts :
- AB=[tex]\sqrt{3^{2}+6^{2} }[/tex] DC=[tex]\sqrt{3^{2}+6^{2} }[/tex]
So AB=DC
- AD=[tex]\sqrt{1^{2}+8^{2} }[/tex] BC=[tex]\sqrt{1^{2}+8^{2} }[/tex]
So AD=BC
SO ABCD IS A PARALLELOGRAM
