Question

Ruby is visiting San Francisco. From her hotel she walks 4 blocks east and 2 blocks north to a coffee shop. Then she walks 5 blocks west and 1 block north to a museum. Where is the museum in relation to her​ hotel?

Answer 1

Answer:

The museum is 1 block west and 3 blocks north from the hotel.

Step-by-step explanation:

First of all, Ruby goes Northeast to a coffe shop, walking 4 blocks to the east and 2 blocks to the north. Then, she goes 5 blocks to the west, and 1 block to the north.

Therefore, she walks:

-3 blocks north

-4 blocks east

-5 blocks west

As east and west are contrary, we have to substract the lower number to the higher one in order to know the difference between both directions (5 W - 4 E = 1 W). As a result, Ruby finally moved west by 1 block.

Finally, we know that the museum is 1 block west and 3 blocks north from the hotel.

Answer 2

I'm not sure if you have done vectors as of yet, but you would first add the x components and y components separately. 

x-components: 4 blocks + 5 block = 9 blocks 
y-component: 2 blocks + 1 block = 3 blocks

Magnitude of this: √(x₂-x₁)²+(y₂-y₁)² 
= √(9)²+(3)²
=√81+9 
=9.5 blocks approx

Angle of of the resultant vector; 

tanθ=y/x 
tanθ=3/9 
θ=tan⁻¹(3/9)
θ=18.43 degrees

Hope I helped :)