the coordinates of a quadrilateral are (1,3), (7,-3), (1,-9), and (-5,-3). Which shape is formed select all that apply-kite-rectangle-rhombus-square-trapezoid

Answer:rectangle , rhombus , and squareStep-by-step explanation:First we find the slope of the line between each pair of points.  We will first name each point:A(1, 3); B(7, -3); C(1, -9); and D(-5, -3).The formula for slope is[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]This means the slope for AB ism = (3--3)/(1-7) = (3+3)/(-6) = 6/-6 = -1The slope for BC ism = (-3--9)/(7-1) = (-3+9)/6 = 6/6 = 1The slope for CD ism = (-9--3)/(1--5) = (-9+3)/(1+5) = (-6)/6 = -1The slope for DA ism = (-3-3)/(-5-1) = (-6)/(-6) = 1If two sides are parallel, then the slopes of their lines are the same.  The slopes of AB and CD are the same; this means they are parallel.  The slopes of BC and DA are the same; this means they are parallel.  This makes this figure a parallelogram.If two sides form a right angle, then their slopes are negative reciprocals.  The slopes of AB and BC are negative reciprocals, so they form a right angle.  The slopes of BC and CD are negative reciprocals, so they form a right angle.  The slopes of CD and AB are negative reciprocals, so they form a right angle.  This means the fourth angle must be a right angle as well.  This makes the figure a rectangle.We next use the distance formula to find the length of each side:[tex]d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]The length of AB is[tex]d=\sqrt{(3--3)^2+(1-7)^2}=\sqrt{6^2+(-6)^2}=\sqrt{36+36}=\sqrt{72}[/tex]The length of BC is [tex]d=\sqrt{(-3--9)^2+(7-1)^2}=\sqrt{6^2+6^2}=\sqrt{36+36}=\sqrt{72}[/tex]The length of CD is[tex]d=\sqrt{(-9--3)^2+(1--5)^2}=\sqrt{(-6)^2+6^2}=\sqrt{36+36}=\sqrt{72}[/tex]The length of DA is[tex]d=\sqrt{(-3-3)^2+(-5-1)^2}=\sqrt{(-6)^2+(-6)^2}=\sqrt{36+36}=\sqrt{72}[/tex]Since all four sides have the same length, the figure is a square.