Question

prove that these are the vertices of the square​

Answer 1

Step-by-step explanation:

Given:

A(3,5) B(6,0) C(1,-3) D(-2,2)

distance between two points (x,y) and (x1,y1) is

√(x1-x)² + (y1-y)²

AB = √( 6-3)² + (0-5)² = √ 9 + 25 = √34

BC = √(6-1)² + (0+3)² = √25 + 9 = √34

CD = √(-2-1)² + (2+3)² = √9 + 25 = √34

AD = √(3+2)² + (5-2)² = √25+ 9 = √34

AC = √(3-1)² + (5+3)² = √ 4 + 64 = √68

BD = √(6+2)² + (0-2)² = √64 + 4 = √68

since,

AB = BC = CD = AD = √34 ans

diagonals AC = BD = √68

Hence, the points are the vertices of a square.

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