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) Β 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= β((x_2- x_1)^2+(y_2- y_1)^2 Β )So, for side ABAB= β((1- 4)^2+(5- 1)^2 Β )= β((-3)^2+(4)^2 Β )= β(9+16)= β25= 5 unitsFor BCBC= β((-3- 1)^2+(2- 5)^2 Β )= β((-4)^2+(-3)^2 Β )= β(16+9)= β25= 5 unitsFor CDBC= β((0-(-3))^2+(-2-2)^2 Β )= β((0+3)^2+(-4)^2 Β )= β(9+16)= β25= 5 unitsFor ADAD= β((0-4)^2+(-2-1)^2 Β )= β((-4)^2+(-3)^2 Β )= β(16+9)= β25= 5 unitsAs all the sides are equalAB=BC=CD=AD= 5 unitsSo the quadrilateral is a square.2 dot.