Ohio Assessments for Educators (OAE) Mathematics Practice Exam

For a matrix to translate along the y-axis, how is it represented mathematically?

1. y + y1, y2, yn

2. x + x1, x2, xn

3. y - y1, y2, yn

4. x - x1, x2, xn

The correct answer is: y + y1, y2, yn

When analyzing how a matrix performs translations along the y-axis, it's important to understand the concept of coordinate transformations in linear algebra. A translation involves shifting points in a coordinate system by a certain amount. For a matrix or transformation to translate points along the y-axis, you need to alter only the y-coordinate of each point while leaving the x-coordinate unchanged. This means you would add a specific value to the y-coordinates of the points in your matrix to shift them upward or downward. The representation should reflect that the translation affects the y-coordinates. The correct mathematical representation for translating points along the y-axis is adding a constant value (let’s denote it as \( y1 \)) to each y-coordinate. This can be represented as: y + y1, y2, yn, where \( y \) is the original y-coordinate and \( y1 \) is the amount of translation. In summary, the mathematical representation of translating along the y-axis focuses on modifying the y-coordinates while keeping the x-coordinates constant, which corresponds directly to the correct choice.