The vertex and anti-vertex represent involuntary actions and experiences over which we have no control. Therefore, the vertex/anti-vertex are tied more to fate and karmic patterns. The vertex is an indicator of the kind of people who may be the momentum behind important changes in our lives.
It also represents innate qualities that are not being used, as well as karmic circumstances that must be dealt with. The anti-vertex represents those qualities that others can see in us that we are not aware of, as well as our abilities to become more aware of those talents.
The vertex will fall into either the 5th, 6th, 7th or 8th house** of the birth chart, with the following emphasis (**A very rare 4th or 9th house Vertex is possible if the birth location is at an extremely high or low latitude. I answered a few people on this in comments): For a 3/9: I would consider a strong attachment to siblings, a need for short trips as a lifestyle (perhaps living in a camper or travel vehicle), or a display or array of computers around one's work place, and an affiliation with a religious organization or highly philosophical ideal, an interest for a country that is noted for mountainous terrain, an identification with law enforcement practice or legal authority, and long-distance endurance sports. For a 4/10, the home would be emphasized, along with family, one parent, security, and a base foundation when the Vertex is in the 4th house, and the career and projects of influence, fame, and status when the Anti-Vertex is placed in the 10th, where one could work on team endeavors--perhaps like associating with a sports team but not being a major influence--for instance, a loyal fan who enthusiastically participates in activities before games and shows great enthusiasm with displays of attention during the event.
A 5th house vertex is "The Lover," (because the 5th house is ruled by Leo). These people are very creative by nature, with great artistic ability. Romance and love are very important to them, and they fall in and out of love, looking for that "special person" in their life. A weakness is that the 5th house vertex person becomes neglectful of all else in their life except for their ideal of love.
A 5th house vertex will yield an 11th house anti-vertex, which indicates a person who does not realize that they are more accepted and wanted by the many friends that they have made. The individual must accept those things in themselves that others appreciate and recognize. Once they accept their social skills and the potential that can come forward in working with others, they will realize that they are more goal-oriented than they understood.
The 6th house vertex is "The Worker," (because the 6th house is ruled by Virgo). There is a strong need to be of service to others, and a need to seek out experiences and circumstances to help others. Work is extremely important, with emphasis placed on detail and precision in career obligations. There can be activities that require specific talents, often in the fields of health and medicine (because of Virgo's rulership of the 6th house).
A 6th house vertex will yield a 12th house anti-vertex. The 12th house corresponds to our subconscious mind, and therefore these individuals are very psychic and attuned to their intuition. Attempts to attune oneself through meditation to the Higher Mind is very important, as the subconscious mind can overpower the conscious mind. This can cause confusion in actions, and these people should always go with their feelings.
A 7th house vertex is "The Partner," (because the 7th house is ruled by Libra). Marriage and partnerships are very important to these people, and contentment in marriage is needed for true happiness. Balance in relationships, both personal and professional, are needed for the individual to explore ideas and obtain valuable insights for critical decisions. These people must have peace and balance in their lives, and they feel lost without someone else with whom to interact.
A 7th house vertex will yield a 1st house anti-vertex, and the enterprising, originating side of the Partner will arise. This will bring forward an Arian-like nature, wanting to start new objectives and ideas, to "get the ball rolling." This person gains much personal satisfaction by the knowledge that they were the driving force to start a new project. Once this person realizes the importance of initiating projects independently of others, they will gain great strength and accomplishment.
An 8th house vertex is "The Mystic," (because the 8th house is ruled by Scorpio). This person is involved with the exploration of the occult, the hidden secrets and mysteries of Life and Death. This person may become involved with the study of yoga, astrology, meditation into past lives, or other metaphysical studies. There will be an undercurrent of strong psychic abilities, physical and sexual power and regeneration, and the ability to overcome extreme obstacles and setbacks in life. These individuals are intense and expressive in their desire for their personal will to see their goals carried through. There can also be outward circumstances as well as personal actions that make them change themselves in a dramatic, powerful way.
An 8th house vertex will yield a 2nd house anti-vertex. This indicates a person who is subconsciously materialistic and involved with finances, personal belongings, and valuables. This individual will find themselves facing occasional periods of difficulties in earning a living or maintaining a certain level of material comfort. During these times, the person will be forced to evaluate their image of self-worth and a positive self-concept.