This is a multipart question about
a vector on a diagram. Consider the vector in the given
diagram. What are the coordinates of its
terminal point? What are the coordinates of its
initial point? And what are the components of the
The first part asks about the
terminal point of the vector; this is the point which the vector is pointing to —
the end of the vector. We can see that the 𝑥-coordinate
of this point is five and the 𝑦-coordinate is one. And so the coordinates of the
terminal point are 5, 1. It’s a very similar story with the
initial point. This is the point from which the
vector starts or comes from. And we can see that its
𝑥-coordinate is one and its 𝑦-coordinate is two.
Finally, what are the components of
the vector? There are two components of the
vector, and it’s written very much like a point is, except instead of using
parentheses, we have angled brackets. The first number tells us how far
right of the initial point the terminal point is. By counting the squares, we can see
that this is four.
The second component tells us how
far up the vector is pointing — how far up the terminal point is from the initial
point. We have to go down by one unit,
which is the same as going up by negative one unit. Our second component is therefore
negative one. So the components of our vector are
four, negative one.
Can you see the link between the
components of the vector and the coordinates of the terminal and initial point? The first coordinate of the
terminal point five minus the first coordinate of the initial point one is equal to
the first component of the vector four. Likewise, the second coordinate of
the terminal point, the 𝑦-coordinate one, minus the second coordinate of the
initial point, the 𝑦-coordinate two, is equal to the second component of the
vector, negative one.
This isn’t a coincidence. To get from the initial point to
the terminal point, you have to move from the 𝑥-coordinate one to the 𝑥-coordinate
to five, moving five minus one equals four units to the right. And you have to move from a
𝑦-coordinate of two to a 𝑦-coordinate of one, which means moving one minus two
equals negative one unit upwards or one unit downwards.