Question Video: Using Initial and Terminal Points to Find the Components of a Vector Represented Graphically | Nagwa Question Video: Using Initial and Terminal Points to Find the Components of a Vector Represented Graphically | Nagwa

Question Video: Using Initial and Terminal Points to Find the Components of a Vector Represented Graphically Mathematics • First Year of Secondary School

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Consider the vector in the diagram. What are the coordinates of the terminal point? What are the coordinates of the initial point? What are the components of the vector?

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Video Transcript

Consider the vector in the diagram. What are the coordinates of the terminal point? What are the coordinates of the initial point? And what are the components of the vector?

For the first part of the question, we recall that when a vector is represented in a coordinate plane, the terminal point is the point at the end of the line segment in the direction of the arrow. We can think of this as where the vector is pointing. And from the diagram, we see that this has coordinates negative seven, negative one.

Similarly, for the second part, the initial point is the point from which the line segment starts, the arrow being directed away from it. From the diagram, we see that this has coordinates negative one, positive two.

For the final part, we’re asked to find the components of the vector. And for this, we recall that the components of a vector from an initial point 𝐴 with coordinates 𝑥 one, 𝑦 one to terminal point 𝐵 with coordinates 𝑥 two, 𝑦 two are the differences between the 𝑥- and 𝑦-coordinates, respectively.

In our case then, the 𝑥-component or the horizontal component 𝑎 is equal to negative seven minus negative one. That’s the difference between the two 𝑥-components, terminal 𝑥 minus initial 𝑥, and that’s negative six. Similarly, for the 𝑦- or vertical component, we have negative one minus two. That’s the difference between the terminal and initial 𝑦-values, and that’s equal to negative three. Hence, the components of the given vector are negative six and negative three. And hence, the terminal point of the given vector is negative seven, negative one. The initial point is negative one, two. And the components of the vector are negative six and negative three.

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