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:

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


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


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