Question

The area of a square with one of its vertices as (5,-2) and mid point of the diagonal as (3, 2) is (in sq. units)

Answer 1

Answer:

16 unit^2

Step-by-step explanation:

Let the point opposite to (5, -2) be (a, b).

As (3, 2) is mid point of (5, - 2) and (a, b), using mid point formula:

⇒ (3, 2) = (5+a/2 , -2+b/2)

⇒ 3 = (5 + a)/2 ; 2 = (-2 + b)/2

⇒ 6 = 5 + a   ; 4 = - 2 + b

⇒ 1 = a    ;   6 = b

   (a, b) = (1, 6)

(5, - 2) and (1, 6) forms a diagonal.

length of diagonal =√(5-1)²+(-2+6)²

                           = √4²+ 4² = 4√2

In general,

diagonal = side√2    , here

⇒ 4√2 = side√2

⇒ 4 = side

     Hence area = side² = 4²

                          = 16

Answer 2

Answer:

$\huge\fcolorbox{black}{aqua}{Solution:-}$

Diagonal of square=root 2 (side)

5root 2 =root2 (side)

side=5cm

area of square=(side)^2=25cm^2