Question

show that the points (-3 5) (3 1) (0 3) and (-1 -4) do not form a quadrilateral

Answer 1

divide the quadrilateral in two triangles and the sum of their areas will be zero, or line may be formed. Hence their is no quadrilateral with area = 0.

Answer 2

concepts : if ABCD is a quadrilateral.

then, slope of AB ≠ slope of BC

similarly, slope of BC ≠ slope of CD

slope of CD ≠ slope of AD

I mean, slope of two consecutive sides of a quadrilateral doesn't have equal value.

here, we assume A(-3,5), B(3,1) , C(0,3) and D(-1,-4)

slope of AB = (1 - 5)/(3 + 3) = -4/6 = -2/3

slope of BC = (3 - 1)/(0 - 3) = -2/3

here, slope of AB = slope of BC

from above concept, ABCD isn't a quadrilateral.

hence, (-3 5) (3 1) (0 3) and (-1 -4) do not form a quadrilateral.