Beasy is driving in his car to take care of some errands. The first errand has him driving to a coffee shop 2 km East and 6 km North of his starting location. Once he
completes that errand, he drives to a thrift store which is 4 km East of the first errand.
What is the displacement of the car from the starting point, rounded to the nearest
km?

From the question, Beasy drives 2km East and 6 km North. He then drives 4 km East of the first errand. An illustrative diagram is shown in the attachment below.

From the diagram S is the starting starting point, C is coffee shop and T is the thrift store.

The displacement of the car from the starting point is giving by /TS/ in the diagram. To calculate /TS/, consider the right-angled triangle TSQ, /TS/ is the hypotenuse.

From The Pythagorean theorem, in a right-angled triangle, the square of the longest side (hypotenuse) equals sum of the squares of the other two sides.

That is,

/TS/² = /SQ/² + /TQ/²

But /TQ/ = /CP/ = 6km

and /SQ/ = /SP/ + /PQ/

/SP/ = 2 km, /PQ/ = 4 km

∴ /SQ/ = 2 km + 4 km

/SQ/ = 6 km

Hence,

/TS/² = 6² + 6²

/TS/² = 36 + 36

/TS/² = 72

/TS/ =

/TS/ = 8.485 km

/TS/ ≅ 8 km ( to the nearest km)

Hence, the displacement of the car from the starting point rounded to the nearest km is 8 km.

Learn more about displacement here: link

At this point in the story, Beasy has driven his car (2+6+4) = 12 km.

He is parked at the thrift store, (2+4) = 6 km East and 6 km North of his starting point.

As the crow flies, the thrift store is √(6km² + 6km²) in a straight line from the starting point.

That's √(72 km²) , which works out to 8.485 km .  When rounded to the nearest whole km, he can phone up his wife and tell her he's "eight kilometers from home can you hear me now ?".

Displacement is a vector, so to answer the question completely, we also need to state its direction.

The angle from home to the thrift store, relative to East, is arctan(6km/6km).

That's 45 degrees.  

The full displacement vector is 8.485 km Northeast.