Question

1. the graph of polygon abcd is shown. graph the image of abcd after a reflection across the line x = 3. include the line of reflection. then write the coordinates of the image.

Explanation:

Step1: Identify the coordinates of ABCD

Assume \(A(1,3)\), \(B(- 1,1)\), \(C(-1,-2)\), \(D(1,-2)\)

Step2: Use the reflection formula

The formula for reflecting a point \((x,y)\) across the line \(x = a\) is \((2a - x,y)\). Here \(a = 3\).
For point \(A(1,3)\): \(x_1=2\times3 - 1=5\), \(y_1 = 3\), so \(A'(5,3)\)
For point \(B(-1,1)\): \(x_2=2\times3-(-1)=7\), \(y_2 = 1\), so \(B'(7,1)\)
For point \(C(-1,-2)\): \(x_3=2\times3-(-1)=7\), \(y_3=-2\), so \(C'(7,-2)\)
For point \(D(1,-2)\): \(x_4=2\times3 - 1=5\), \(y_4=-2\), so \(D'(5,-2)\)

Step3: Graph the reflection

Graph the line \(x = 3\) (a vertical line passing through \(x = 3\) on the \(x\) - axis). Then plot the original polygon \(ABCD\) and its image \(A'B'C'D'\)

Answer:

The coordinates of the image are \(A'(5,3)\), \(B'(7,1)\), \(C'(7,-2)\), \(D'(5,-2)\)