The coordinates of the vertices of quadrilateral ABCD are A(4,1) B(1,5) C(-3,2) and D(0,-2). Prove the quadrilateral is a square.
Accepted Solution
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Answer:The quadrilateral is a SQUARE.Step-by-step explanation:GivenFour pointsA(4,1) B(1,5)C(-3,2)D(0, -2)The quadrilateral formed will be ABCD with sides AB, BC, CD, AD. In order to prove if a quadrilateral is a square we have to prove that all sides of the quadrilateral are equal.We will use the two-point distance formula to calculate lengths of sides of quadrilateral.The distance formula:d= √((x_2- x_1)^2+(y_2- y_1)^2 )So, for side ABAB= √((1- 4)^2+(5- 1)^2 )= √((-3)^2+(4)^2 )= √(9+16)= √25= 5 unitsFor BCBC= √((-3- 1)^2+(2- 5)^2 )= √((-4)^2+(-3)^2 )= √(16+9)= √25= 5 unitsFor CDBC= √((0-(-3))^2+(-2-2)^2 )= √((0+3)^2+(-4)^2 )= √(9+16)= √25= 5 unitsFor ADAD= √((0-4)^2+(-2-1)^2 )= √((-4)^2+(-3)^2 )= √(16+9)= √25= 5 unitsAs all the sides are equalAB=BC=CD=AD= 5 unitsSo the quadrilateral is a square.2 dot.