Question

2 a figure and a line of reflection are shown. draw the image of the figure after it is reflected across the line.

Explanation:

Step1: Identify key points

Find the vertices of the original figure. Let's assume the original figure has vertices (let's name them A, B, C, D for clarity) on the grid.

Step2: Reflect each point

For a vertical line of reflection (the given line is vertical), the reflection of a point \((x,y)\) across a vertical line \(x = a\) is \((2a - x,y)\). Calculate the distance of each vertex from the line of reflection, then plot the reflected point on the opposite side at the same distance.

Step3: Connect the reflected points

Once all vertices are reflected, connect them in the same order as the original figure to form the reflected image.

(Note: Since this is a drawing task, the key is to use the property of reflection over a vertical line: each point's x - coordinate is mirrored over the line, while the y - coordinate remains the same. For example, if a vertex is 1 unit to the right of the line, its reflection is 1 unit to the left of the line with the same y - value.)

Answer:

To draw the reflected figure:

1. Locate each vertex of the original (shaded) figure.
2. For each vertex, measure its horizontal distance from the vertical line of reflection.
3. Plot a new point on the opposite side of the line, at the same horizontal distance (so the x - coordinate is mirrored, y - coordinate stays).
4. Connect these new points to form the reflected image (mirror image across the vertical line).

(Visually, the reflected figure will be a mirror - image of the original across the vertical line, with corresponding vertices equidistant from the line.)