Question

a group 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 represented on the coordinate plane. what distance will the rover cover if it completes one circuit? a. 36 meters

Explanation:

Step1: Find length of AB

Points A(2, 11) and B(4, 11). Using distance formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1 = 2,y_1 = 11,x_2 = 4,y_2 = 11$, so $AB=\sqrt{(4 - 2)^2+(11 - 11)^2}=\sqrt{2^2+0^2}=2$.

Step2: Find length of BC

Points B(4, 11) and C(16, 2). $BC=\sqrt{(16 - 4)^2+(2 - 11)^2}=\sqrt{12^2+( - 9)^2}=\sqrt{144 + 81}=\sqrt{225}=15$.

Step3: Find length of CD

Points C(16, 2) and D(2, 2). $CD=\sqrt{(2 - 16)^2+(2 - 2)^2}=\sqrt{( - 14)^2+0^2}=14$.

Step4: Find length of DA

Points D(2, 2) and A(2, 11). $DA=\sqrt{(2 - 2)^2+(11 - 2)^2}=\sqrt{0^2+9^2}=9$.

Step5: Calculate perimeter

The perimeter of the path (distance covered in one circuit) is $AB + BC+CD + DA=2+15 + 14+9=40$.

Answer:

40 meters