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Lesson 5

1. Lesson 5

1.3. Explore 2

Mathematics 30-3 Module 5

Module 5: Geometry

 

In the next activity, you will look at how a translation can be combined with a dilation.

 

Try This 2

 

Jenara is installing a bathroom sink, and she needs to pass two PEX waterlines and an ABS drainpipe through a wall. The PEX waterline has a nominal size of in and will require a hole of in. The ABS drainpipe has a nominal size of 2 in and will require a hole of 2.5 in.

  1. Determine a scale factor that could be used to dilate the 2.5-in hole to the -in hole.

Jenara has drawn a 2.5-in hole in the wall where she would like to position the ABS drainpipe. Jenara plans to put the centre of one waterline hole 2 in left and 3 in above the centre of the drain line. She plans to put the other waterline hole 2 in right and 3 in above the centre of the drain line.

 

This diagram shows a large circle labelled “Hole for drain” with the centre of a smaller circle 2 in to the left and 3 in above its centre and the centre of a second smaller circle 2 in to the right and 3 in above the large centre. The two small circles are labelled “Holes for waterlines.”

 

Suppose Jenara has drawn the drainpipe on a coordinate grid and plans to use a translation and a dilation to draw the circles required for the waterlines.

  1. To draw the waterline holes, do you expect it will be easier to translate and then dilate or to dilate and then translate the drain-line hole? Explain your reasoning.

    This diagram shows a circle with a radius of 1.25 centred at the point (0, 0.)
  2. Sketch the diagram using the Grid Paper Template located in the course Toolkit or grid paper that you may already have. Draw four points on the circle that you can use to help with the transformation. Label the points A, B, C, and D.
  3. Complete tables like the ones shown for the right waterline hole using the points you determined in question 3.

    Point

    Original Point Dilated by Factor from Question 1

    Dilated Point Translated

    A(__, __)

     

     

    B(__, __)

     

     

    C(__, __)

     

     

    D(__, __)

     

     

    Point

    Original Point Translated

    Translated Point Dilated by Factor from Question 1

    A(__, __)

     

     

    B(__, __)

     

     

    C(__, __)

     

     

    D(__, __)

     

     
  4. If the two tables in question 4 resulted in different coordinates, which do you expect to be correct? Use what you think are the correct coordinates to draw the coordinates for the right waterline on the grid.
  5. Describe at least two ways a transformation or transformations can be used to determine the coordinates for the left waterline hole.
  6. Use one of the methods you described in question 6 to draw the left waterline hole.

course folder Save your responses in your course folder.

 

Share 1

 

With a partner or in a group, discuss the following questions.

  1. Describe another method Jenara could have used to accurately make the holes.
  2. Describe some advantages and disadvantages of using transformations to draw the positions of the holes in this scenario.

course folder If required, place a summary of your discussion in your course folder.

You can use either the drain hole or the other waterline hole as a starting point.
To dilate a point about the origin, multiply each x- and y-coordinate by the scale factor. To translate a point, change x to move horizontally (left or right) and y to move vertically (up or down).
A(−1.25, 0), B(0,1.25), C(1.25, 0), and D(0, −1.25) are good points to work with.
Divide the new size by the original size to determine the scale factor. Converting to a decimal first may make this easier.