Question

What is the perimeter of a triangle with vertices of (5,1) (-3,3) (-7,-3)

Answer 1

`Vertices:\\ A(5,1)\\B(-3,3)\\C(-7,-3)\\\\ You\ must\ find\ length\ of\ AB,\ BC,\ AC.\\\\ A(5,1)\ \ \ \ \ \ B(-3,3)\\\\Distance\ between\ A \ and\ B:\\AB=√((x_B-x_A)^2+(y_A-y_B)^2)\\\\AB=√((-3-5)^2+(3-1)^2)\\AB=√(8^2+2^2)\\AB=√(64+4)\\AB=√(68)`
`B(-3,3)\ \ \ \ C(-7,-3)\\\\Distance\ between\ B \ and\ C:\\BC=√((x_C-x_B)^2+(y_C-y_B)^2)\\\\BC=√((-7-(-3))^2+(-3-3)^2)\\BC=√((-4)^2+(-6)^2)\\BC=√(16+36)\\BC=√(52)`
`A(5,1)\ \ \ \ \ \ C(-7,-3)\\\\Distance\ between\ A \ and\ C:\\AC=√((x_C-x_A)^2+(y_C-y_A)^2)\\\\AC=√((-7-5)^2+(-3-1)^2)\\AC=√((-12)^2+(-4)^2)\\AC=√(144+16)\\AC=√(160)`
`Perimeter\ of\ triangle=\ AB+AC+BC=\\√(68)+√(52)+√(160)=2√(17)+2√(13)+2√(40)`