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.

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=√((d-b)^2+((c-a)^2)`

`KI=√((2-0)^2+(2-0)^2)=√(4+4)=√(8)=2√(2)\ units`

`KT=√((5-0)^2+(-5-0)^2)=√(25+25)=√(50)=5√(2)\ units`

`TE=√((7-5)^2+(-3+5)^2)=√(4+4)=√(8)=2√(2)\ units`

`IE=√((7-2)^2+(-3-2)^2)=√(25+25)=√(50)=5√(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=√((5-2)^2+(-5-2)^2)=√(3^2+7^2)=√(9+49)=√(58)\ units`

`KE=√((7-0)^2+(-3-0)^2)=√(7^2+3^2)=√(9+49)=√(58)\ units`

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

It means KIET is a rectangle.