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.

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.

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