Question

the coordinates of the vertices of a rectangle in order are (5,2), (-1,4), (-2,1) and (4,-1). what is the perimeter of the rectangle to the nearest tenth of a unit​

Answer 1

19 units

Explanation:

Plot points A(5,2), B(-1,4), C(-2,1) and D(4,-1) on the coordinate plane. Find lengths of all sides as distances between two points:

`AB=√((-1-5)^2+(4-2)^2)=√(6^2+2^2)=√(36+4)=√(40)=2√(10)\ units\\ \\BC=√((-2-(-1))^2+(1-4)^2)=√(1^2+3^2)=√(1+9)=√(10)\ units\\ \\CD=√((4-(-2))^2+(-1-1)^2)=√(6^2+2^2)=√(36+4)=√(40)=2√(10)\ units\\ \\DA=√((5-4)^2+(2-(-1))^2)=√(1^2+3^2)=√(1+9)=√(10)\ units`

The perimeter of the rectangle ABCD is

`AB+BC+CD+DA=2√(10)+√(10)+2√(10)+√(10)=6√(10)\approx 18.97\ units\approx 19\ units`