Question

Show the points a(2,-2),b (14,10), c(11,13) and d (-1,1) are tge vertices of a rectangle

Answer 1

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Answer 2

Answer.

✺RECTANGLE.
A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also opposite sides are parallel and of equal length.


so. find the above points as a vertex of rectangle .

✺STEP 1 (distance between two point)

let. the triangle be ABCD

so according to definition opposite side are equal mean AB=CD, BC=AD


✍ so for prove this we have to find distance between two point .


✦DISTANCE BETWEEN. (AB)

A=(2,-2). B= (14,10)

=>
$\sqrt{ {(x(2) - x(1)) }^{2} + {(y(2) - (y1))}^{2} }$

$= > \sqrt{ {(14 - 2)}^{2} + {(10 - ( - 2))}^{2} }$




$\sqrt{ {12 }^{2} + {12}^{2} }$


$\sqrt{144 + 144}$


$= \sqrt{288}$

✦DISTANCE BETWEEN ( CD)

C=(11,13). D=(-1,1)

USING DISTANCE FORMULA✔✔


$= > \sqrt{ {( - 1 - 11)}^{2} + {(1 - 13)}^{2} }$


=>
$\sqrt{ {( - 12)}^{2} + {( - 12)}^{2} }$



$\sqrt{144 + 144}$



$= \sqrt{288}$



=> AB=CD


SIMILARLY WE PROVE ANOTHER OPPOSITE SIDE.


HENCE THE ABOVE PROOF ARE ACCORDING TO RECTANGLE .


✔SO WE CAN SAY THAT a(2,-2),b (14,10), c(11,13) and d (-1,1) are vertices of a rectangle.

✍ because opposite side are equal.