Question

what is true about the coordinates of a point and its image after a reflection across the y - axis? the x - coordinates are opposites. the y - coordinates are the same

Explanation:

Step1: Analyze the \(x\)-coordinates

Take point \(E(-3,4)\) and its image \(E'(3,4)\). The \(x\)-coordinate of \(E\) is \(-3\) and of \(E'\) is \(3\). Similarly, for \(F(-1,4)\) and \(F'(1,4)\), \(G(-2,1)\) and \(G'(2,1)\), \(H(-4,3)\) and \(H'(4,3)\). We can see that if a point \((x,y)\) is reflected across the \(y\)-axis, its image is \((-x,y)\). So the \(x\)-coordinates are opposites.

Step2: Analyze the \(y\)-coordinates

Looking at the \(y\)-coordinates of each pair: for \(E(-3,4)\) and \(E'(3,4)\) the \(y\)-coordinate is \(4\); for \(F(-1,4)\) and \(F'(1,4)\) the \(y\)-coordinate is \(4\); for \(G(-2,1)\) and \(G'(2,1)\) the \(y\)-coordinate is \(1\); for \(H(-4,3)\) and \(H'(4,3)\) the \(y\)-coordinate is \(3\). So the \(y\)-coordinates are the same.

Answer:

The \(x\)-coordinates are opposites. The \(y\)-coordinates are the same.