Question

Find the length of the rectangle whose vertices are given.

A(2, 1), B(5, 4), C(0, 3), D(3, 6)

Answer 1

Length of rectangle? Or Area or perimeter?

Answer 2

In order to find the lengths of the rectangle, use distance formula and find the distances between AB, BC, CD and AD.

Answer 3

So...
\[l(AB)=\sqrt{(2-5)^2+(1-4)^2}=\sqrt{(-3)^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}\]

\[l(BC)=\sqrt{(5-0)^2+(4-3)^2}=\sqrt{(5)^2+(1)^2}=\sqrt{25+1}=\sqrt{26}\]

\[l(CD)=\sqrt{(0-3)^2+(3-6)^2}=\sqrt{(-3)^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}\]

\[l(AD)=\sqrt{(2-3)^2+(1-6)^2}=\sqrt{(-1)^2+(-5)^2}=\sqrt{1+25}=\sqrt{26}\]
From Above results we can see that
l(AB)=l(ACD) & l(BC)=l(AD)
i.e. opposite sides are congruent