Question

A recycling truck begins its weekly route at the recycling plant at point A, as pictured on the coordinate plane below. It travels from point A to point B, then points C, D, and E, respectively, before returning to the recycling plant at point A at the end of the day. The truck’s route is illustrated on the coordinate plane below. If each unit on the coordinate plane represents one mile, what is the total distance the truck travels on its route?
A. 41

B. 38

C. 13

D. 5

(The picture of the graph should be there, I apologize if it isn't clear enough. Also, please explain the answer in detail, I want to try to understand it so when I approach a problem like this, I will know what to do)

Answer 1

Answer:

41

Step-by-step explanation:

Answer 2

Answer:

• B. 38

Step-by-step explanation:

• Use Pythagorean theorem to find line lengths

We see the figure formed by the route is symmetric and

• BC = EA
• CD= DE

The total distance is the perimeter of the polygon

1. AB is horizontal line, 2 units long (from -1 to 1)

• 1 - (-1)  = 2 miles

2. BC = √((5-1)²+(2 -(-1))²) = √(16 + 9)= √25 = 5 miles

• EA = BC = 5 miles

3. CD = √(13-2)² + (5-1)²) = √121+16 = √137 = 11.7 miles

• DE = CD = 11.7 miles

Total

• 2 + 5*2 + 11.7*2 = 35.4 miles

Close option is option B