Distance & Midpoint ProjectMonica 10.2

[1] Drop map into Geogebra.

[2] Use the "Create Line Segment" function to make a line segment between Jakarta and the first stop on your trip.

This creates two coordinate points in Geogebra. They take these two points and determine the distance and midpoint between them.

[3] Round to nearest tenths.

[4] You need to show five legs and thus requiring 5 distances and 5 midpoints. The point values have significant figures in the hundredths (it is a quite a challenge if they don't have a calculator).

[5] You only need to show your use of the two formulas on the first leg of the trip.

Road Trip Itinerary

Jakarta → Bandung → Yogyakarta → Malang → Surabaya → Semarang → Jakarta

[1] Jakarta → Bandung

Jakarta: (54.2, 88.2)Bandung: (80,60)

distance = √(54.2 - 80)² + (88.2 - 60)²= √(-25.8)² + (28.2)²= √665.6 + 795.2= √1460.8= 38.2 units

[2] Bandung → Yogyajakarta [3] Yogyajakarta → Malang

midpoint = 54.2 + 80 , 88.2 + 60

2 2 = (67.1, 74.1)

Bandung: (80, 60)Yogya: (173.1, 31.1)

Yogya: (173.1, 31.1)Malang: (249.6, 23.2)

distance = √(80 - 173.1)² + (60 - 31.1)²= √(-93.1)² + (28.9)²= √8667.6 + 835.2= √9502.8= 97.5 units

distance = √(173.1 - 249.6)² + (31.1 - 23.2)²= √(-76.5)² + (7.9)²= √5852.3 + 62.3= √5914.7= 76.9 units

midpoint = 80 + 173.1 , 60 + 31.1

2 2 = (126.6, 45.6)

midpoint = 173.1 + 249.6 , 31.1 + 23.2

2 2 = (211.4, 27.2)

[4] Malang → Surabaya [5] Surabaya → Semarang [6] Semarang → Jakarta

Malang: (249.6, 23.2) Surabaya: (253.6, 47.6)

Surabaya: (253.6, 47.6) Semarang: (175.3, 58)

Semarang: (175.3, 58)Jakarta: (54.2, 88.2)

distance = √(249.6 - 253.6)² + (23.2 - 47.6)²= √(-4)² + (-24.4)²= √16 + 595.4= √611.4= 24.7 units

distance = √(253.6 - 175.3)² + (47.6 - 58)²= √(78.3)² + (-10.4)²= √6130.9 + 108.2= √6239.1= 78.9 units

distance = √(175.3 - 54.2)² + (58 - 88.2)²= √(121.1)² + (-30.2)²= √14665.2 + 912= √15577.2= 124.8 units

midpoint = 249.6 + 253.6 , 23.2 + 47.6

2

= (251.6, 35.4)

2

midpoint = 253.6 + 175.3 , 47.6 + 58

2

= (214.5, 52.8)

2

midpoint = 175.3 + 54.2 , 58 + 88.2

2

= (114.8, 73.1)

2

1

2

3

4

5

6

Semarang: (175.3, 58)Jakarta: (54.2, 88.2)Distance = 124.8 unitsMidpoint = (114.8, 73.1) Surabaya: (253.6, 47.6)

Semarang: (175.3, 58)Distance = 78.9 unitsMidpoint = (214.5, 52.8)

Malang: (249.6, 23.2)Surabaya: (253.6, 47.6)Distance = 24.7 unitsMidpoint = (251.6, 35.4)

Yogya: (173.1, 31.1)Malang: (249.6, 23.2)Distance = 76.9 unitsMidpoint = (211.4, 27.2)

Bandung: (80, 60)Yogya: (173.1, 31.1)Distance = 97.5 unitsMidpoint = (126.6, 45.6)

Jakarta: (54.2, 88.2)Bandung: (80,60)Distance = 38.2 unitsMidpoint = (67.1, 74.1)

My Java Road Trip