Question

Prove that (3, 2), (5, 4), (3, 6) and (1, 4) taken in order form a square. Find the area of the square​

Answer 1

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

d= √(x2-x1)^2 + (y2-y1)^2

AB=√(5-3)^2 + (4-2)^2

=√4+4

=√2×4.

=2√2

BC=√(3-5)^2 + (6-4)^2

=√4+4

=√2×4

=2√2

CD=√(1-3)^2 + (4-6)^2

=√4+4

=√2×4

=2√2

DA=√(3-1)^2 + (2-4)^2

=√4+4

=√2×4

=2√2

AC=√(3-3)^2 + (6-2)^2

=√0+16

=4

BD=√(1-5)^2 + (4-4)^2

=√16+0

=4

AB=BC=CD=DA and AC=BD. all the four sides of the quadrilateral ABCD are equal and its diagonals AC and BD ate also equal. Therefore, ABCD is a square