Question

MUG has coordinates M(9,-6), U(2,7), and G(4,3). A translation maps point M to M'(6,-3). What are the coordinates of U' and G' for this translation? (type an ordered pair) U'=_____ G'=_____​

Answer 1

To find the coordinates of U' and G', we need to know the vector of the translation. This vector is the change in position from M to M'. The coordinates of M and M' are (9, -6) and (6, -3) respectively.

We can calculate the translation vector as follows:
Subtract the coordinates of M from the coordinates of M'.

This gives us:
M_prime - M = (6 - 9, -3 - (-6)) = (-3, 3)
So, the translation vector is (-3, 3).

Now, to find the coordinates of U' and G', we need to apply this translation to the coordinates of U and G.

This is done by adding the translation vector to the coordinates of U and G as follows:

For U:
U_prime = U + translation vector = (2, 7) + (-3, 3) = (-1, 10)
So, the coordinates of U' are (-1, 10).

And for G:
G_prime = G + translation vector = (4, 3) + (-3, 3) = (1, 6)
So, the coordinates of G' are (1, 6).

Thus upon translating the points using the translation vector (-3, 3), we achieve the coordinates of points U' and G' as (-1, 10) and (1, 6) respectively. The end result doesn't depend on the chosen point - any point transferred by this vector will move exactly as other points, and that's the main property of the translation transformation. That's why we can be sure about correctness of the acquired result.