Which of the following is the area of a quadrilateral with vertices at (-4,2),(1,2),(1,-3) and (-4,-3)A)20units^2 B)25units^2C)31units^2D)36units^2

Answer:The correct option is B.Step-by-step explanation:The given vertices are (-4,2),(1,2),(1,-3) and (-4,-3).Plot these point on a coordinate plate. From the graph it is noticed that the given quadrilateral is a square.Distance formula:[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Use distance formula to find the side length.[tex]AB=\sqrt{(1-(-4))^2+(2-2)^2}=\sqrt{5^2}=5[/tex][tex]BC=\sqrt{(1-1)^2+(-3-2)^2}=\sqrt{(25}=5[/tex]Since both consecutive sides are equal therefore it is a square.Area of a square is[tex]A=a^2[/tex]Where, a is side length.The side length of the square is 5. So, area of ABCD is[tex]A=(5)^2[/tex][tex]A=25[/tex]Therefore the area of quadrilateral is 25 units square. Option B is correct.