Question

1. reinforce you plan to walk from home along the indicated route. you will start at home, go to school, to the library, to the park, and back home again.

a. fill in the missing coordinates on the graph representing your route.
b. find the distance of your route.
c. find the area of the city surrounded by your route. show or explain your process.

Explanation:

Step1: Identify missing coordinates

1. The point connected to School (6,0) and Library (-7,2) is a horizontal/vertical match: same x as School (6), same y as Library (2) → (6,2)
2. The point connected to Home (0,0) and Park (-7,-3) is a horizontal/vertical match: same x as Home (0), same y as Park (-3) → (0,-3)

Step2: Calculate segment lengths

• Home to School: $|6-0| = 6$
• School to (6,2): $|2-0| = 2$
• (6,2) to Library (-7,2): $|-7-6| = 13$
• Library (-7,2) to Park (-7,-3): $|-3-2| = 5$
• Park (-7,-3) to (0,-3): $|0-(-7)| = 7$
• (0,-3) to Home (0,0): $|0-(-3)| = 3$

Step3: Sum lengths for total route

Total distance = $6 + 2 + 13 + 5 + 7 + 3$

Step4: Calculate enclosed area

Treat the shape as a large rectangle minus a smaller rectangle:
Large rectangle bounds: x from -7 to 6, y from -3 to 2. Area = $(6 - (-7)) \times (2 - (-3)) = 13 \times 5 = 65$
Small rectangle bounds: x from 0 to 6, y from -3 to 0. Area = $(6-0) \times (0 - (-3)) = 6 \times 3 = 18$
Enclosed area = $65 - 18 = 47$

Answer:

a. Missing coordinates:

• Top right point (between School and Library): $(6,2)$
• Bottom middle point (between Park and Home): $(0,-3)$

b. Total route distance: $36$

c. Enclosed area: $47$