Question

The coordinates of the vertices of a quadrilateral are R(-1,3), S(3,3), T(5,-1), and U(-2,-1). Find the perimeter of the quadrilateral. Round to the nearest tenth.

Answer 1

The distance between 2 points P(a,b) and Q(c,d) is given by the formula:


`|PQ|= \sqrt{ (a-c)^(2) + (b-d)^(2) }`

thus, the lengths of the sides of the quadrilateral can be calculated using the distance formula:


`|RS|= \sqrt{ (-1-3)^(2) + (3-3)^(2)}=√( 16 + 0)=4` units



`|ST|= \sqrt{ (3-5)^(2) + (3-(-1))^(2) }=√( 4+16)=4.47` units



`|TU|= \sqrt{ (5-(-2))^(2) + (-1-(-1))^(2) }=√( 49 + 0)=7` units



`|RU|= \sqrt{ (-1-(-2))^(2) + (3-(-1))^(2) }=\sqrt{ (1)^(2) + (4)^(2) }=4.12` units

The perimeter of RSTU is 4+4.47+7+4.12=19.6


Answer: 19.6 units