Question

answer attempt 4 out of 10
coordinates of k: (3, 1)
coordinates of k: (-3, -1)
when a point is reflected over the y-axis, the dropdown changes sign.

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is that the \(x\) - coordinate changes its sign, and the \(y\) - coordinate remains the same. But in the given problem, we can see that for point \(K(3,1)\) and its image \(K'(- 3,-1)\), if we consider reflection over the origin (since both \(x\) and \(y\) coordinates change sign), but the question is about reflection over \(y\) - axis. Wait, maybe there is a mis - step. Wait, the correct rule for reflection over \(y\) - axis: If a point \((x,y)\) is reflected over the \(y\) - axis, the new point is \((-x,y)\). But in the given \(K(3,1)\) and \(K'(-3,-1)\), both \(x\) and \(y\) changed sign, which is reflection over the origin. But the question is about reflection over \(y\) - axis. However, the blank is asking what changes sign when reflecting over \(y\) - axis. The correct answer for reflection over \(y\) - axis is the \(x\) - coordinate. But in the given coordinates, maybe there is a typo, but following the question's context, when reflecting over \(y\) - axis, the \(x\) - coordinate changes sign.

Step2: Confirm the rule

The formula for reflection over \(y\) - axis: For a point \(P(x,y)\), the image \(P'(-x,y)\). So the \(x\) - coordinate (the first coordinate) changes sign.

Answer:

\(x\) - coordinate (or "the \(x\) - coordinate" or "the first coordinate")