L1 Drawing a Dilation
Completion requirements
Unit A: Geometry
Chapter 2: Transformations
Drawing a Dilation
If a scale factor is given, it is possible to draw the dilation of the object or shape.
An image of a hexagon is three times larger than the original regular hexagon. The side lengths are equal, and each angle has a measure of 120°.
a.
Explain how the original hexagon and its image are proportional.
b.
Draw the regular hexagon three times larger than it appears.
a.
Each corresponding side length in the image will be three times larger than the original, and the angles measures will remain 120°.
b.
Step 1: Find the centre of the figure. Identify the key points of the figure. For the hexagon, the key points are the six vertices.
Step 2: Find the distance from the centre to each vertex of the polygon. Since the hexagon is regular, the distance from the centre to each vertex will be the same.
Step 3: Multiply the distance to each vertex by the scale factor of 3.
1.5 cm × 3 = 4.5 cm
Step 4: Draw a 4.5 cm line from the centre, passing through each vertex. It is best to use a pencil so that you can erase the lines when you are done.
Step 5: Connect each key point (vertex) to form the dilated hexagon. The green hexagon is the enlargement.
Step 6: Erase the lines, if you wish.
The green hexagon is three times larger than the original black hexagon.
Step 2: Find the distance from the centre to each vertex of the polygon. Since the hexagon is regular, the distance from the centre to each vertex will be the same.
Step 3: Multiply the distance to each vertex by the scale factor of 3.
1.5 cm × 3 = 4.5 cm
Step 4: Draw a 4.5 cm line from the centre, passing through each vertex. It is best to use a pencil so that you can erase the lines when you are done.
Step 5: Connect each key point (vertex) to form the dilated hexagon. The green hexagon is the enlargement.
Step 6: Erase the lines, if you wish.
The green hexagon is three times larger than the original black hexagon.