Question

Perimeter the coordinates of the vertices of a quadrilateral are R(-1,3), S(3,3), T(5,-1), and U(-2,-1)

Answer 1

Answer:

The perimeter is equal to $P=(11+2\sqrt{5}+\sqrt{17})\ units$  or $P=19.59\ units$

Step-by-step explanation:

we have

The coordinates of the vertices are

R(-1,3), S(3,3), T(5,-1), and U(-2,-1)

plot the figure to better understand the problem

see the attached figure

we know that

The perimeter of a quadrilateral is the sum of its four length sides

so

$P=RS+ST+TU+UR$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance RS

$R(-1,3)\\S(3,3)$  

substitute the values

$d=\sqrt{(3-3)^{2}+(3+1)^{2}}$

$d=\sqrt{(0)^{2}+(4)^{2}}$

$RS=4\ units$

step 2

Find the distance ST  

$S(3,3)\\T(5,-1)$  

substitute the values

$d=\sqrt{(-1-3)^{2}+(5-3)^{2}}$

$d=\sqrt{(-4)^{2}+(2)^{2}}$

$ST=2\sqrt{5}\ units$

step 3

Find the distance TU

$T(5,-1)\\U(-2,-1)$  

substitute the values

$d=\sqrt{(-1+1)^{2}+(-2-5)^{2}}$

$d=\sqrt{(0)^{2}+(-7)^{2}}$

$TU=7\ units$

step 4

Find the distance UR  

$U(-2,-1)\\R(-1,3)$  

substitute the values

$d=\sqrt{(3+1)^{2}+(-1+2)^{2}}$

$d=\sqrt{(4)^{2}+(1)^{2}}$

$UR=\sqrt{17}\ units$

step 5

Find the perimeter

$P=RS+ST+TU+UR$

substitute the values

$P=4+2\sqrt{5}+7+\sqrt{17}$

$P=(11+2\sqrt{5}+\sqrt{17})\ units$ -----> exact value

$P=(11+4.47+4.12)=19.59\ units$ -----> approximate value