Question

in a reflection each point of the preimage and its corresponding point on the image are the same distance from the line of reflection. the segment that connects a point on the preimage to its corresponding point on the image is perpendicular to the line of reflection
example 2 (continued)
reflection in the x - or y - axis
check the image matches the prediction.
discussion question
when a point is reflected over the x - axis, how can you find its coordinates?
study tip
what is preserved?
because it is a rigid motion, all lengths and angle measures are preserved in a reflection.

Explanation:

When a point \((x,y)\) is reflected over the \(x -\)axis, the \(x -\)coordinate remains the same because the horizontal position relative to the \(x -\)axis does not change. The \(y -\)coordinate changes its sign. This is based on the geometric property of reflection over the \(x -\)axis. For example, if we have a point \((a,b)\), its reflection over the \(x -\)axis is \((a,-b)\) as the distance from the \(x -\)axis for the original point \((a,b)\) (which is \(|b|\)) and for the reflected point \((a, - b)\) (which is \(|-b|=|b|\)) is the same.

Answer:

If a point has coordinates \((x,y)\), its coordinates after reflection over the \(x -\)axis are \((x,-y)\).