Question

26 what is the equation of the line across which the preimage was reflected? the line was reflected across the line blank

Explanation:

Step1: Recall Reflection Over x - axis

When a figure is reflected over the x - axis, the transformation rule is \((x,y)\to(x, - y)\). But we can also check the mid - point between a point and its image. For a reflection over the x - axis, the mid - point of a point \((x,y)\) and its image \((x, - y)\) lies on the x - axis (\(y = 0\)), and the x - axis is the perpendicular bisector of the segment joining a point and its image after reflection over the x - axis.

Step2: Analyze the Graph

Looking at the image and the pre - image, we can observe the vertical positions of the corresponding points. The image is above the x - axis and the pre - image is below the x - axis (or vice - versa). The line of reflection should be the x - axis, because when we reflect a point over the x - axis, the y - coordinate changes sign. By looking at the grid, the distance from the image points to the x - axis and the pre - image points to the x - axis is equal, which confirms that the line of reflection is the x - axis, whose equation is \(y=0\).

Answer:

\(y = 0\)