Question

a point with a positive x-coordinate and a negative y-coordinate is reflected over the y-axis. which sentence describes the coordinates of the new point? the x-coordinate is negative, and the y-coordinate is negative. the x-coordinate is positive, and the y-coordinate is negative. the x-coordinate is negative, and the y-coordinate is positive. the x-coordinate is positive, and the y-coordinate is positive.

Explanation:

Step1: Recall reflection over y - axis rule

When a point \((x,y)\) is reflected over the \(y\) - axis, the rule for the transformation is \((x,y)\to(-x,y)\).

Step2: Analyze the original point's coordinates

The original point has a positive \(x\) - coordinate (let's say \(x = a\) where \(a>0\)) and a negative \(y\) - coordinate (let's say \(y=-b\) where \(b > 0\)).

Step3: Apply the reflection rule

Using the reflection over \(y\) - axis rule \((x,y)\to(-x,y)\), substituting \(x = a\) (positive) and \(y=-b\) (negative) into the rule, we get the new point as \((-a,-b)\). So the \(x\) - coordinate of the new point is negative (\(-a<0\)) and the \(y\) - coordinate is negative (\(-b < 0\)).

Answer:

The \(x\) - coordinate is negative, and the \(y\) - coordinate is negative.