Question

find the image of (1,2) after a reflection about the x-axis followed by a reflection about the y-axis.
grid with (1,2) and axes from -3 to 3
(?, )
enter the number that belongs in the green box.

Explanation:

Step1: Reflect over x - axis

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\). For the point \((1,2)\), after reflection over the \(x\) - axis, the point becomes \((1,-2)\).

Step2: Reflect over y - axis

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\). Now, take the point \((1, - 2)\) from the previous step. After reflection over the \(y\) - axis, we substitute \(x = 1\) into \(-x\), so the \(x\) - coordinate becomes \(-1\) and the \(y\) - coordinate remains \(-2\). So the final point is \((-1,-2)\). The value in the green box (the \(x\) - coordinate) is \(-1\).

Answer:

\(-1\)