Question

Prove that the quadrilateral defined by the points M(2,4), I(1,2), L(5,1), K(4,−1) is a parallelogram. Which Formula did you select and Why?

Answer 1

The given points isn't define a parallelogram.

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 =
`√((x 2 - x 1)^2 + (y 2 - y 1)^2)`

On substituting the given values, we get

=
`√((1 - 2)^2 + (2- 4)^2)`

=
`√(1+4)`

=
`√(5)`

IL =
`√((x 3 - x 2)^2 + (y 3 - y 2)^2)`

=
`√((5-1)^2+(1-2)^2)`

=
`√(16+1)`

=
`√(17)`

LK =
`√((x 4 - x 3)^2 + (y 4 - y 3)^2)`

=
`√((4-5)^2+(-1-1)^2)`

=
`√(1+4)`

=
`√(5)`

KM =
`√((x 4 - x 1)^2 + (y 4 - y 1)^2)`

=
`√((4-2)^2+(-1-4)^2)`

=
`√(4+25)`

=
`√(29)`

Here, MI = LK = √5

IL ≠ KM