This is what I think they are

1."Leaving their native land to colonize in America," they expected to land in the colony of Virginia.
A.prepositional phrase B. appositive phrase c.participial phrase d.gerund phrase e.infinitive phrase f.absolute phrase

2."Steering a northerly course," the captain sailed the ship to the rocky coast of New England instead.
A.prepositional phrase B. appositive phrase c.participial phrase d.gerund phrase e.infinitive phrase f.absolute phrase

3."Landing in New England" caused much disappointment among the Pilgrims.
A.prepositional phrase B. appositive phrase c.participial phrase d.gerund phrase e.infinitive phrase f.absolute phrase

4.Today, homes "on Cape Cod" still display this famous weathered look.
A.prepositional phrase B. appositive phrase c.participial phrase d.gerund phrase e.infinitive phrase f.absolute phrase

I think 1.a 2.a 3.b 4.b

All are incorrect, sorry. =(

Notice that 1, 2, and 3 all start with words ending in -ing. No preposition has -ing at the end.

Go back and rethink all of these, please.
http://www.jiskha.com/display.cgi?id=1385695339

So now I think 1,2,3 are all gerund phrases because a gerund is a verb form that ends in -ing

Almost right! Yes, #3 is a gerund phrase. Here's why:

Landing in New England is serving as the subject of the main verb, caused.

In 2 and 3, however, both -ing phrases are describing (modifying) the subjects of the sentences.
Who was "leaving their native land"?
Who was "steering a northerly course"?

Let me know what you think for 2, 3, and 4.

Sorry ... #3 is a gerund phrase. #s 1 and 2, as well as 4, are the ones you need to rethink.

I would say 1.b 2.e 4.e

Infinitive phrases begin with "to" verb forms: to walk, to read, etc.

I don't see any absolute phrases here.

1.e 2.b 4.a

You're pretty much guessing on 1 and 2.

4 is now correct.

Let's go through each of the sentences and analyze the phrases:

1. "Leaving their native land to colonize in America," they expected to land in the colony of Virginia.

The phrase "Leaving their native land to colonize in America" is a participial phrase because it starts with a present participle verb form "Leaving" and functions as an adjective, modifying the subject "they."

So, the correct answer for this sentence is: c. participial phrase.

2. "Steering a northerly course," the captain sailed the ship to the rocky coast of New England instead.

The phrase "Steering a northerly course" is a participial phrase because it starts with a present participle verb form "Steering" and functions as an adjective, modifying the subject "the captain."

So, the correct answer for this sentence is: c. participial phrase.

3. "Landing in New England" caused much disappointment among the Pilgrims.

The phrase "Landing in New England" is a gerund phrase because it starts with a gerund verb form "Landing" and functions as the subject of the sentence.

So, the correct answer for this sentence is: d. gerund phrase.

4. Today, homes "on Cape Cod" still display this famous weathered look.

The phrase "on Cape Cod" is a prepositional phrase because it starts with the preposition "on" and functions as an adjective, modifying the noun "homes."

So, the correct answer for this sentence is: a. prepositional phrase.

Therefore, the correct answers are:
1. c. participial phrase
2. c. participial phrase
3. d. gerund phrase
4. a. prepositional phrase