Question

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

Answer 1

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.
Distance between the points is given by
$\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$
$\therefore AB=\sqrt{{(-3-3)}^2+{(5-1)}^2}$
$=\sqrt{{(-6)}^2+(4{)}^2}$
$=\sqrt{36+16}=\sqrt{52}=2\sqrt{13}$
$BC=\sqrt{{(3-0)}^2+{(1-3)}^2}$
$=\sqrt{(3{)}^2+(-2{)}^2}=\sqrt{9+4}=\sqrt{13}$
$CD=\sqrt{{(0-(-1\left)\right)}^2+{(3-(-4\left)\right)}^2}$
$=\sqrt{(1{)}^2+(7{)}^2}=\sqrt{1+49}=\sqrt{50}=5\sqrt{2}$
$AD=\sqrt{{(-3-(-1\left)\right)}^2+{(5-(-4\left)\right)}^2}$
$=\sqrt{(-2{)}^2+(9{)}^2}=\sqrt{4+81}=\sqrt{85}$
It can be observed that all sides of this quadrilateral are of different lengths. Therefore, it can be said that it is only a general quadrilateral, and not any specific type such as square, rectangle, etc.