1) The vector v = [-6, -2] has tail "A" and head "B". Graph each point "A", and determine the coordinates of "B".
a) A(8, 5)
How would I find the coordinates of B for the question?
Do you find it by adding the x values together and the y values together?
So. . .the coordinate of "B" for a) is. . .
B(2, 3) ?
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2) Point A(5, -3) is the head of vector v. Graph each vector v and determine the coordinates of its tail.
a) v = [8, -5]
Do I subtract the coordinate values with one another, so the tail for question a is (3, -2)?
To find the coordinates of point B in question 1), you need to add the components of vector v to the coordinates of point A.
Since the vector v is given as [-6, -2], you add -6 to the x-coordinate of point A and -2 to the y-coordinate of point A.
For question a), with point A(8, 5) and vector v([-6, -2]):
B(x-coordinate of B) = 8 + (-6) = 2
B(y-coordinate of B) = 5 + (-2) = 3
So the coordinates of point B are B(2, 3). You are correct!
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For question 2), in order to find the tail of vector v, you need to subtract the components of vector v from the coordinates of its head, which is point A.
Since the vector v is given as [8, -5], you subtract 8 from the x-coordinate of point A and -5 from the y-coordinate of point A.
For question a), with point A(5, -3) and vector v([8, -5]):
Tail(x-coordinate of tail) = 5 - 8 = -3
Tail(y-coordinate of tail) = -3 - (-5) = 2
So the coordinates of the tail of vector v are (-3, 2). You are correct!
In summary, to find the coordinates of a point based on a vector, you add or subtract the components of the vector from the coordinates of the given point.