"“And now also,” said the prophet, “the ax is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire.” Not by its name, but by its fruit, is the value of a tree determined. If the fruit is worthless, the name cannot save the tree from destruction. John declared to the Jews that their standing before God was to be decided by their character and life. Profession was worthless. If their life and character were not in harmony with God's law, they were not His people. DA 107.1"
"And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire."
The EGW passage directly quotes and elaborates on the imagery of the axe laid to the root of the trees, making it a clear and explicit allusion to Matthew 3:10.
"Wherefore by their fruits ye shall know them."
The EGW passage directly applies the principle of judging by fruits, as stated in Matthew 7:20, to the Jews' standing before God. It's a clear application of the principle, not just a thematic similarity.
"Under his heart-searching words, his hearers were convicted. They came to him with the inquiry, “What shall we do then?” He answered, “He that hath two coats, let him impart to him that hath none; and he that hath meat, let him do likewise.” And he warned the publicans against injustice, and the soldiers against violence. DA 107.2 All who became the subjects of Christ's kingdom, he said, would give evidence of faith and repentance. Kindness, honesty, and fidelity would be seen in their lives. They would minister to the needy, and bring their offerings to God. They would shield the defenseless, and give an example of virtue and compassion. So the followers of Christ will give evidence of the transforming power of the Holy Spirit. In the daily life, justice, mercy, and the love of God will be seen. Otherwise they are like the chaff that is given to the fire. DA 107.3"
"And the people asked him, saying, What shall we do then?"
EGW directly quotes the question from Luke 3:10 and elaborates on the implications of John the Baptist's answer.
"“our God is a consuming fire.” Hebrews 12:29 . In all who submit to His power the Spirit of God will consume sin. But if men cling to sin, they become identified with it. Then the glory of God, which destroys sin, must destroy them. Jacob, after his night of wrestling with the Angel, exclaimed, “I have seen God face to face, and my life is preserved.” Genesis 32:30 . Jacob had been guilty of a great sin in his conduct toward Esau; but he had repented. His transgression had been forgiven, and his sin purged; therefore he could endure the revelation of God's presence. But wherever men came before God while willfully cherishing evil, they were destroyed. At the second advent of Christ the wicked shall be consumed “with the Spirit of His mouth,” and destroyed “with the brightness of His coming.” 2 Thessalonians 2:8 . The light of the glory of God, which imparts life to the righteous, will slay the wicked. DA 107.4"
"And Jacob called the name of the place Peniel: for I have seen God face to face, and my life is preserved."
EGW directly quotes Genesis 32:30 and builds an argument around it.
"And then shall that Wicked be revealed, whom the Lord shall consume with the spirit of his mouth, and shall destroy with the brightness of his coming:"
Ellen White directly references 2 Thessalonians 2:8 in this passage.