"Three of the coordinates of the parallelogram STUV are S(-2,-2), T(7,7) and U(5,15). State the vector ST and hence determine the coordinates of V."
So I've figured out that ST = (9,9), but I don't see how that helps me find V.
If you draw it out, it becomes obvious that the vector ST is the same as UV. If ST has a velocity vector of 9,9 then you can find the coordinates of V.
V = (5-9, 15-9)
(5, 15 are coordinates of U)
V = (-4, 6)
To find the coordinates of point V, we need to use the fact that opposite sides of a parallelogram are equal and parallel.
Since ST is a vector that represents the displacement from point S to point T, we can use it to find the coordinates of point V by translating point U in the opposite direction.
To do this, we subtract the coordinates of vector ST from the coordinates of point U.
Given that ST = (9,9), we can subtract it from the coordinates of point U, which are (5,15):
V = U - ST
= (5,15) - (9,9)
= (5 - 9, 15 - 9)
= (-4, 6)
Therefore, the coordinates of point V are V(-4, 6).
To find the coordinates of V, we can use the fact that the opposite sides of a parallelogram are equal in length and parallel to each other.
Since ST is a vector that represents the displacement from point S to point T, we can use this vector to find the coordinates of V.
The coordinates of S are given as (-2,-2), and we know that the vector ST is (9,9).
To find the coordinates of V, we can start at S and move in the direction of the vector ST.
Starting at S, we add the x-component of the vector ST to the x-coordinate of S, and add the y-component of the vector ST to the y-coordinate of S.
So, the x-coordinate of V is -2 + 9 = 7, and the y-coordinate of V is -2 + 9 = 7.
Therefore, the coordinates of V are (7,7).