Question

Alanah is picking up two friends to go to a concert. She drives from her house to pick up Mia, then she drives to pick up Teresa, and then they go to the arena to see the concert. Answer the questions to find the total distance of Alanah's trip to the arena. When necessary, round answers to the nearest tenth.​

Answer 1

1. Find the distance from Alanah's house to Mia's house. Show your work.

Alanah (2,8) Mia (8,16) √( (8 - 2)² + (16 - 8)² ) = 10 Distance from Alanah to Mia is 10 units

2. What is the distance from Mia's house to Teresa's house? Explain how you found this distance. Write your answer in the space below. √( (8 - 8)­² + (2 - 16)² ) = 14 distance from Mia to Teresa is 14 units

3. Find the distance from Teresa's house to the arena. Show your work.

Write your answer in the space below. √( (14 - 8)² + (4 - 2)² ) = 6.3 ≈ 6

4. What is the total distance of Alanah's trip to the arena?

Write your answer in the space below. 10 + 14 + 6 = 30 30 units is the total distance of the trip

Explanation:

Answer 2

Total distance = 30.3 units

Explanation:

Coordinates for the location of Alanah, Mia, Teresa and Arena are,

Alanah → (2, 8)

Mia → (8, 16)

Teresa → (8, 2)

Arena → (14, 4)

Distance between two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by the formula,

d =
`√((y_2-y_1)^2+(x_2-x_1)^2)`

Distance between Alanah and Mia =
`√((16-8)^2+(8-2)^2)`

=
`√(100)`

= 10 units

Distance between Mia and Teresa =
`√((16-2)^2+(8-8)^2)`

= 14 units

Distance between Teresa and Arena =
`√((4-2)^2+(14-8)^2)`

=
`√(40)`

= 6.3 units

Total distance of Alanah's trip to Arena = 10 + 14 + 6.3

= 30.3 units