Name the type or quadrilateral formed, if any, by the following points and give reasons for your answer:
(- 3, 5), (3, 1), (0, 3), (- 1, - 4)

Question

Name the type or quadrilateral formed, if any, by the following points and give reasons for your answer:(- 3, 5), (3, 1), (0, 3), (- 1, - 4)

Philoid · Accepted Answer

Given points are A(- 3, 5), B(3, 1), C(0, 3) and D(- 1, - 4).

Let us find the lengths of the sides.

We know that the distance between the points (x₁, y₁) and (x₂, y₂) is .

Now,

⇒

We got AB≠BC≠CD≠DA, this may be a quadrilateral which is not of standard shape.

Now we find the lengths of the diagonals.

⇒

⇒ AC + BC = AB

We got points ABC are collinear.

∴ The points doesn’t form a quadrilateral.