ΔCAR has coordinates C (2, 4), A (1, 1), and R (3, 0). A translation maps point C to C' (3, 2). Find the coordinates of A' and R' under this translation.

A' (4, -2); R' (2, -1)

A' (-2, 2); R' (2, -2)

A' (2, -1); R' (4, -2)

A' (-1, 0); R' (-2, 2)

Question

ΔCAR has coordinates C (2, 4), A (1, 1), and R (3, 0). A translation maps point C to C' (3, 2). Find the coordinates of A' and R' under this translation.

 A' (4, -2); R' (2, -1)

 A' (-2, 2); R' (2, -2)

 A' (2, -1); R' (4, -2)

 A' (-1, 0); R' (-2, 2)

anonymous · Answer

If this is translation, that means that the triangle's only been moved a certain distance in each direction, right? Find the difference between C and C', and apply it to each point.
$$T=\left( \Delta x,\Delta y \right) = \left( 1,-2 \right)$$$$A'=A+T$$$$R'=R+T$$