Answer:
The given points isn't define a parallelogram.
Step-by-step explanation:
As we know,
⇒ The opposite sides of a parallelogram are equal.
The given points are:
(x1, y1) = M(2,4)
(x2, y2) = I(1,2)
(x3, y3) = L(5,1)
(x4, y4) = K(4,−1)
Now,
On applying the Distance formula, we get
MI = [tex]\sqrt{(x 2 - x 1)^2 + (y 2 - y 1)^2}[/tex]
On substituting the given values, we get
= [tex]\sqrt{(1 - 2)^2 + (2- 4)^2}[/tex]
= [tex]\sqrt{1+4}[/tex]
= [tex]\sqrt{5}[/tex]
IL = [tex]\sqrt{(x 3 - x 2)^2 + (y 3 - y 2)^2}[/tex]
= [tex]\sqrt{(5-1)^2+(1-2)^2}[/tex]
= [tex]\sqrt{16+1}[/tex]
= [tex]\sqrt{17}[/tex]
LK = [tex]\sqrt{(x 4 - x 3)^2 + (y 4 - y 3)^2}[/tex]
= [tex]\sqrt{(4-5)^2+(-1-1)^2}[/tex]
= [tex]\sqrt{1+4}[/tex]
= [tex]\sqrt{5}[/tex]
KM = [tex]\sqrt{(x 4 - x 1)^2 + (y 4 - y 1)^2}[/tex]
= [tex]\sqrt{(4-2)^2+(-1-4)^2}[/tex]
= [tex]\sqrt{4+25}[/tex]
= [tex]\sqrt{29}[/tex]
Here, MI = LK = √5
IL ≠ KM
