**Graphing reflections :**

To reflect a figure across a line of reflection, reflect each of its vertices. Then connect the vertices to form the image. Each point and its image must be at the same distance from the line of reflection.

The following properties of reflections would be much useful for you to reflect a figure across a line of reflection.

**The following are the three basic properties of reflections :**

1. The image and the pre-image are of the same size and shape. So they are congruent.

2. The line segment which connects the corresponding parts of the image and pre-image is perpendicular to the line of reflection.

3. The distance from the line of reflection of the corresponding parts of the image and pre-image is the same.

**Example 1 : **

Triangle ABC has the vertices A(1, -3), B(4, -1) and C(6, -5). Graph the triangle ABC and its image after a reflection across the x-axis.

**Solution :**

**Step 1 : **

Sketch the triangle ABC with the vertices A(1, -3), B(4, -1) and C(6, -5).

**Step 2 :**

Reflect the vertex A.

Point A is 3 units below the x-axis. Count 3 units above the x-axis and plot point A'.

**Step 3 :**

Reflect the vertex B.

Point B is 1 unit below the x-axis. Count 1 unit above the x-axis and plot point B'.

**Step 4 :**

Reflect the vertex C.

Point C is 5 units below the x-axis. Count 5 units above the x-axis and plot point C'.

**Step 5 : **

**Sketch the image (A'B'C') of the triangle ABC using the above steps. **

**Example 2 : **

A pentagon has the vertices A(-5, 6), B(-3, 6), C(-2, 4), D(-3, 1) and E(-5,1). Graph the pentagon and its image after a reflection across the y-axis.

**Solution :**

**Step 1 :**

Sketch the pentagon with the vertices A(-5, 6), B(-3, 6), C(-2, 4), D(-3, 1) and E(-5,1).

**Step 2 :**

Reflect the vertex A.

Point A is 5 units away from y-axis on the left side. Count 5 units from y-axis on the right side and plot point A'.

**Step 3 :**

Reflect the vertex B.

Point B is 3 units away from y-axis on the left side. Count 3 units from y-axis on the right side and plot point B'.

**Step 4 :**

Reflect the vertex C.

Point C is 2 units away from y-axis on the left side. Count 2 units from y-axis on the right side and plot point C'.

**Step 5 :**

Reflect the vertex D.

Point D is 3 units away from y-axis on the left side. Count 3 units from y-axis on the right side and plot point D'.

**Step 6 :**

Reflect the vertex E.

Point E is 5 units away from y-axis on the left side. Count 5 units from y-axis on the right side and plot point E'.

**Step 5 : **

**Sketch the image of the triangle using the above steps. **

After having gone through the stuff given above, we hope that the students would have understood "Graphing reflections".

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