Question

graph the image of trapezoid abcd after a reflection over the y - axis.

Explanation:

Step1: Find coordinates of vertices

First, identify the coordinates of trapezoid \(ABCD\) vertices. From the graph:

• \(A(-4, 1)\)
• \(B(-2, 1)\)
• \(C(-6, 9)\)
• \(D(-9, 9)\)

Step2: Apply reflection over \(y\)-axis

The rule for reflection over the \(y\)-axis is \((x, y) \to (-x, y)\). Apply this to each vertex:

• For \(A(-4, 1)\): New \(A' = (4, 1)\)
• For \(B(-2, 1)\): New \(B' = (2, 1)\)
• For \(C(-6, 9)\): New \(C' = (6, 9)\)
• For \(D(-9, 9)\): New \(D' = (9, 9)\)

Step3: Plot the new vertices

Plot points \(A'(4, 1)\), \(B'(2, 1)\), \(C'(6, 9)\), \(D'(9, 9)\) on the coordinate plane and connect them to form the reflected trapezoid.

Answer:

The reflected trapezoid \(A'B'C'D'\) has vertices at \((4, 1)\), \((2, 1)\), \((6, 9)\), and \((9, 9)\) (plotted by reflecting each original vertex over the \(y\)-axis using the rule \((x, y) \to (-x, y)\)).