Question

If A(0,3), C(-2,5) are the opposite vertices of a
square , then the area of the square is

Answer 1

Answer:

4

Step-by-step explanation:

As these are opposite vertices, the line joining these points will be the diagonal of the square.

So,

Distance between A and C = length of diagonal of square

Using Distance formula:

= > diagonal = √[ ( - 2 - 0 )² + ( 5 - 3 )² ]

= √( 2² + 2² )

= √(4+4)

= √8

= 2√2

By Pythagoras theorem: let the length of side be a so:

= > side^2 + side^2 = diagonal^2

= > 2side^2 = (2√2)^2

= > 2side^2 = 8

= > side^2 = 8/2 = 4

Area of square = side^2

= > side^2 = 4 = area of square