Question

determine the line of reflection that maps the pre - image segment ab to the image segment ab.

Explanation:

Step1: Find coordinates of points

Let's assume coordinates of \(A\) as \((x_1,y_1)\) and \(B\) as \((x_2,y_2)\), and \(A'\) as \((x_1',y_1')\) and \(B'\) as \((x_2',y_2')\). From the graph, if \(A=(1, - 1)\), \(B=(3,-4)\), \(A'=(-1,-1)\), \(B'=(-3,-4)\).

Step2: Use reflection formula

The formula for reflection over the line \(x = 0\) (y - axis) is \((x,y)\to(-x,y)\). For point \(A(1,-1)\), after reflection over \(x = 0\), we get \(A'(-1,-1)\). For point \(B(3,-4)\), after reflection over \(x = 0\), we get \(B'(-3,-4)\)

Answer:

\(x = 0\)