If a point is translated by (3, 4), what are the new coordinates of point (2, 2)?

When a point undergoes a translation, its coordinates are adjusted based on the values provided in the translation vector. In this case, the translation vector is (3, 4), which means that the x-coordinate will increase by 3 units and the y-coordinate will increase by 4 units.

Starting with the original point (2, 2):

• To find the new x-coordinate, we add 3 to the original x-coordinate:

(2 + 3 = 5).

• To find the new y-coordinate, we add 4 to the original y-coordinate:

(2 + 4 = 6).

Therefore, after the translation, the new coordinates of the point are (5, 6).

This process illustrates how translation works in a Cartesian coordinate system by shifting the position of a point based on specified values for both axes. The calculation reflects the combined effect of moving the point to a new position in the defined direction and distance. Hence, the new coordinates resulting from the translation are indeed (5, 6).