Find the distance between the two points in simplest radical form.(5,−9) and (−3,−1)

Answer:The distance between the points ( 5 , - 9 ) and ( - 3 , - 1 ) is 4[tex]\sqrt{8}[/tex] Step-by-step explanation:Given points as :Point A = ( 5 , - 9 )I.e (x_1 , y_1) = ( 5 , - 9 )Point B = ( - 3 , - 1 )I.e( x_2 , y_2) =  ( - 3 , - 1 )Let The distance between points A and B = ABSo From distance formulaDistance AB = [tex]\sqrt{(y_2 - y_1)^{2} + (x_2 - x_1)^{2}}[/tex]So, Distance AB = [tex]\sqrt{( - 1 + 9)^{2} + ( - 3 - 5)^{2}}[/tex]Or, Distance AB = [tex]\sqrt{(8)^{2} + (- 8)^{2}}[/tex]Or, Distance AB = [tex]\sqrt{64 + 64}[/tex]Or, Distance AB = [tex]\sqrt{128}[/tex]∴ Distance AB = 4[tex]\sqrt{8}[/tex]Hence The distance between the points ( 5 , - 9 ) and ( - 3 , - 1 ) is 4[tex]\sqrt{8}[/tex]  Answer