Agroup of college students built a self-guided rover and tested it on a plane surface. they programmed the vehicle to move along the path
a–b–c–d–a shown on the coordinate plane. what distance will the rover cover if it completes one circuit?

36 meters
40 meters
54 meters
60 meters
68 meters

The answer is 40 meters

Using the formula √(x2-x1)²+(y2-y1)²  on each line to get the distance, then adding them together to get the total perimeter.

line AB=2

(2,11) (4,11)

√(4-2)²+(11-11)²

√4

2

line BC=15

(4,11) (16,2)

√(16-4)²+(2-11)²

√12²+(-9)²

√144+81

√225

15

line CD=14

(16,2) (2,2)

√(2-16)²+(2-2)²

√(-14)²+(0)²

√196

14

line AD=9

(11,2) (2,2)

√(2-11)²+(2-2)²

√-9²+0²

√81

9

Since line AB=2, BC=15, CD=14, and AD=9.

2+15+14+9=40

giving you a final answer of 40 meters

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value