Question

Determine the most precise name for KIET (parallelogram,rhombus,rectangle or square.) you must use slope or length. K(0,0) I(2,2) T(5,-5) E(7,-3)

Answer 1

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 $A(a,b)$ and $B(c,d)$: $AB=\sqrt{(d-b)^2+((c-a)^2}$

$KI=\sqrt{(2-0)^2+(2-0)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units$

$KT=\sqrt{(5-0)^2+(-5-0)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units$

$TE=\sqrt{(7-5)^2+(-3+5)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units$

$IE=\sqrt{(7-2)^2+(-3-2)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units$

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]

$IT=\sqrt{(5-2)^2+(-5-2)^2}=\sqrt{3^2+7^2}=\sqrt{9+49}=\sqrt{58}\ units$

$KE=\sqrt{(7-0)^2+(-3-0)^2}=\sqrt{7^2+3^2}=\sqrt{9+49}=\sqrt{58}\ units$

IT= KE, i.e. diagonals are equal.

It means KIET is  a rectangle.