Name the type of quadrilateral formed, if any by the following points and give reasons for your answer.
 (-3,5)(1,10),(3,1)(-1,-4)
 

Solution:

Let the points (-3,5),(3,1),(0,3), and (-1,-4) be representing the vertices A,B,C, and D of the given quadrilateral respectively.

$AB =\sqrt{{(-3-3)}^2+{(1-5)}^2 )}$

$=\sqrt{(36+16)}$

$=2\sqrt{13}$

$BC=\sqrt{{(0-3)}^2+{(3-1)}^2 )}$

$=\sqrt{(9+4)}$

$=\sqrt{13}$

$CD=\sqrt{{(-1-0)}^2+{(-4-3)}^2 }$

$=\sqrt{(1+49)}$

$=5\surd 2$

$AD =\sqrt{{(-1+3)}^2+{(-4-5)}^2)}$

$=\sqrt{(4+81})$

$=\sqrt{85}$

It's also seen that points A, B, and C are collinear. So, the given points can only form 3 sides i.e, a triangle and not a quadrilateral which has 4 sides. Therefore, the given points cannot form a general quadrilateral.