Question

prove that the point (- 4, 4,)( 2, - 2)(5, 1) and (-1, 7 )taken in order are the vertices of the rectangle​

Answer 1

Answer:

Yes these points form a rectangle

conditions for formation of rectangle - opposite sides are equal and diagonals bisect each other

in order to find whether oppsosite sides are equal use distance formula and in order to find whether diagonals bisect each other use mid point theorem

Step-by-step explanation:

answer in adjoining figure

Answer 2

yes the given points are the vertices of a rectangle .

Step-by-step explanation:

let the given points are as A(-4,4), B(2,-2), C(5,1) and D(-1,7)

NOW,

      By using the distance formula:

         $d=\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }$

$=>AB=\sqrt{(2+4)^2+(-2-4)^{2} } \\=>AB=6\sqrt{2}$

$=>BC=\sqrt{(5-2)^{2}+(1-4)^{2} } \\=>BC=3\sqrt{2}$

$=>CA=\sqrt{(5+1)^{2}+(7-1)^{2} } \\=>CA=6\sqrt{2}$

$=>DA=\sqrt{(-1+4)^{2}+(7-4)^{2} } \\=>DA=3\sqrt{2}$

       ∵     AB=CA

            BC=DA

Clearly the opposite sides of the quadilateral are equal

Hence the given vertices are the vertices of a rectangle.