If a point (2, 3) is translated by the vector (4, -1), what is the new position?

If a point (2, 3) is translated by the vector (4, -1), what is the new position?

• A. (4, 2)
• B. (6, 2)
• C. (2, -1)
• D. (1, 4)

Answer: (B)

To find the new position of the point (2, 3) after translating it by the vector (4, -1), you add the components of the vector to the coordinates of the point. Starting with the original point (2, 3), you apply the translation vector (4, -1) as follows: - For the x-coordinate: You take the original x-coordinate, which is 2, and add the x-component of the vector, which is 4. So, \( 2 + 4 = 6 \). - For the y-coordinate: You take the original y-coordinate, which is 3, and add the y-component of the vector, which is -1. So, \( 3 + (-1) = 2 \). After performing these calculations, the new position of the point becomes (6, 2). This corresponds to the correct answer, highlighting that proper translation involves straightforward addition of the respective coordinates of the vector to the original point.

To find the new position of the point (2, 3) after translating it by the vector (4, -1), you add the components of the vector to the coordinates of the point.

Starting with the original point (2, 3), you apply the translation vector (4, -1) as follows:

• For the x-coordinate:

You take the original x-coordinate, which is 2, and add the x-component of the vector, which is 4.

So, ( 2 + 4 = 6 ).

• For the y-coordinate:

You take the original y-coordinate, which is 3, and add the y-component of the vector, which is -1.

So, ( 3 + (-1) = 2 ).

After performing these calculations, the new position of the point becomes (6, 2). This corresponds to the correct answer, highlighting that proper translation involves straightforward addition of the respective coordinates of the vector to the original point.