Question

1. reflecting a point on the line of symmetry, implies

p(x, y)--->p(-x, y)
p(x, y)--->p(x, -y)
p(x, y)--->p(-x, -y)
p(x, y)--->p(x, y)

Explanation:

Step1: Reflection over y - axis

When a point \(P(x,y)\) is reflected over the \(y\) - axis, the \(x\) - coordinate changes sign and the \(y\) - coordinate remains the same. So the transformation is \(P(x,y)\to P'(-x,y)\).

Step2: Reflection over x - axis

When a point \(P(x,y)\) is reflected over the \(x\) - axis, the \(y\) - coordinate changes sign and the \(x\) - coordinate remains the same. So the transformation is \(P(x,y)\to P'(x, - y)\).

Step3: Reflection over origin

When a point \(P(x,y)\) is reflected over the origin, both the \(x\) and \(y\) coordinates change sign. So the transformation is \(P(x,y)\to P'(-x,-y)\).

Step4: Identity transformation

\(P(x,y)\to P'(x,y)\) is not a reflection. It is an identity transformation where the point remains in the same position.

Answer:

A. \(P(x,y)\to P'(-x,y)\)