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? distance (meters) distance (meters) a. 36 meters b. 40 meters c. 54 meters d. 60 meters e. 68 meters

Explanation:

Step1: Find length of AB

Points A(2, 11) and B(3, 11). Using distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, here $x_1 = 2,y_1 = 11,x_2=3,y_2 = 11$. So $AB=\sqrt{(3 - 2)^2+(11 - 11)^2}=1$.

Step2: Find length of BC

Points B(3, 11) and C(16, 2). Using distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, $x_1 = 3,y_1 = 11,x_2=16,y_2 = 2$. Then $BC=\sqrt{(16 - 3)^2+(2 - 11)^2}=\sqrt{13^2+(- 9)^2}=\sqrt{169 + 81}=\sqrt{250}=5\sqrt{10}\approx15.8$.

Step3: Find length of CD

Points C(16, 2) and D(2, 2). Using distance formula, $x_1 = 16,y_1 = 2,x_2=2,y_2 = 2$. So $CD=\sqrt{(2 - 16)^2+(2 - 2)^2}=14$.

Step4: Find length of DA

Points D(2, 2) and A(2, 11). Using distance formula, $x_1 = 2,y_1 = 2,x_2=2,y_2 = 11$. So $DA=\sqrt{(2 - 2)^2+(11 - 2)^2}=9$.

Step5: Calculate perimeter

Perimeter $P=AB + BC+CD + DA=1+15.8+14 + 9=39.8\approx40$.

Answer:

B. 40 meters