Answer: rectangle.
Step-by-step explanation:
Given points: K(0,0) I(2,2) T(5,-5) E(7,-3)
Distance formula to find distance between [tex]A(a,b)[/tex] and [tex]B(c,d)[/tex]: [tex]AB=\sqrt{(d-b)^2+((c-a)^2}[/tex]
[tex]KI=\sqrt{(2-0)^2+(2-0)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]
[tex]KT=\sqrt{(5-0)^2+(-5-0)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]
[tex]TE=\sqrt{(7-5)^2+(-3+5)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]
[tex]IE=\sqrt{(7-2)^2+(-3-2)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]
i.e. KI = TE and KT= IE, so opposite sides equal.
It can be a parallelogram or rectangle. [if all sides are equal it would be square or rhombus]
[tex]IT=\sqrt{(5-2)^2+(-5-2)^2}=\sqrt{3^2+7^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]
[tex]KE=\sqrt{(7-0)^2+(-3-0)^2}=\sqrt{7^2+3^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]
IT= KE, i.e. diagonals are equal.
It means KIET is a rectangle.
