Question

Show that the points (-4 ,-1), (-2, -4), (4, 0) and (2, 3) are the verticies points of a rectangle.

Answer 1

Given
let the points be A,B,C,D.
distance between points = $\sqrt{(}(x_2-x_1{)}^2+(y_2-y_1{)}^2)$
so distance of $A{B}^2=(-4-(-2){)}^2+(-1+4{)}^2=13$ units.
Similarly,
distance of $B{C}^2$ = 20 units.
distance of $C{D}^2$ = 13 units
distance of $D{C}^2$ = 20 units
therefore, opp sides are equal
diagonals distance are also equal i.e. AC=BD
diagonals and opp sides are equal they are vertices of rectangle