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

Find the components of the vector 𝐴𝐵, where 𝐴 = (−4.5, 1.2) and 𝐵 = (−4.5, 5.7).

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Video Transcript

Find the components of the vector 𝐴𝐵, where 𝐴 is the point negative 4.5, 1.2 and 𝐵 is the point negative 4.5, 5.7.

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

In our question, the initial point is 𝐴 with coordinates negative 4.5, 1.2 and our terminal point is 𝐵 with coordinates negative 4.5, 5.7. And comparing with the situation, our diagram, we can just read off the values of 𝑥 one, 𝑦 one, 𝑥 two and 𝑦 two and substitute them into the formula we have for the components of the vector: 𝑥 two minus 𝑥 one, 𝑦 two minus 𝑦 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 𝐴𝐵, where 𝐴 is the point negative 4.5, 1.2 and 𝐵 is the point negative 4.5, 5.7, are zero, 4.5.