Why did Rosetta travel 6.5 billion km to reach a comet that was only 510 million km from Earth?

Question

I am reading this news article about the Rosetta mission.

In one paragraph it says:

Philae's data collection from a comet travelling at 18 kilometres (11 miles) per second, currently at a distance of 510 million kilometres (320 million miles) from Earth, crowns a 10-year mission to study the origins of Solar System some 4.6 billion years ago, and maybe even life on Earth.

This means that the comet is about 510 million kilometers distant.

But in the another paragraph it says like this:

Philae landed Wednesday after a nail-biting seven-hour, 20-km descent from Rosetta, which had travelled more than a decade and 6.5 billion kilometres (four billion miles) to meet up with comet 67P/Churyumov-Gerasimenko in August this year

So my question is why did Rosetta traveled this long distance of 6.5 billion kilometers?

Answer 1

It did not travel in a straight line. It passed 4 planets for gravity assist¹ in order to gain the velocity and change to the trajectory² required to meet the comet.

1. See Gravity Assist: Rosetta – Rosetta – first spacecraft to match orbit with a comet for details.
2. The comet is currently approaching the Sun, but further from the Sun than Earth. So effectively the vehicle needed not only to gain speed but flip the direction of travel almost opposite to where it was originally heading.
3. The Rosetta Interactive 3D model shows the route it took - very impressive considering all the gravity assists required incredibly accurate calculations

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Can you please add more information saying why it did not travel in a straight line,why it has to pass 4 planets etc?

Explanation courtesy of TheBlastOne:

If it travelled in a straight line to the comet, it would need to reach a speed (relative to earth) that no launch vehicle can deliver. (Or at least: no launch vehicle could deliver the required acceleration at the time of Rosetta's launch; Ariane was the most powerful launcher available at that time.)