# Question Video: Finding the Component of a Vector Joining Two Points Mathematics • 12th Grade

Find the components of the vector π΄π΅, where π΄ = (β4.5, 1.2) and π΅ = (β4.5, 5.7).

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### Video Transcript

Find the components of the vector π΄π΅, where π΄ is the point negative 4.5, 1.2 and π΅ is the point negative 4.5, 5.7.

The components of a vector with initial point π₯ one, π¦ one and terminal point π₯ two, π¦ two are π₯ two minus π₯ one, π¦ two minus π¦ one. This makes sense because to get from π₯ one, π¦ one to π₯ two, π¦ two, you have to move π₯ two minus π₯ one units to the right and then π¦ two minus π¦ one units up.

In our question, the initial point is π΄ with coordinates negative 4.5, 1.2 and our terminal point is π΅ with coordinates negative 4.5, 5.7. And comparing with the situation, our diagram, we can just read off the values of π₯ one, π¦ one, π₯ two and π¦ two and substitute them into the formula we have for the components of the vector: π₯ two minus π₯ one, π¦ two minus π¦ one.

Substituting those values in, we get negative 4.5 minus negative 4.5, 5.7 minus 1.2. And simplifying each component, we get zero, 4.5. So the components of the vector π΄π΅, where π΄ is the point negative 4.5, 1.2 and π΅ is the point negative 4.5, 5.7, are zero, 4.5.