Learning Resources

Investigation 7: Transformations of Circles

Test yourself

A circle has equation: ( x - 2)² + (y + 3)² = 25

1. The coordinates of the centre are (2 , -3) and length of its radius is 5.
   
   
2. Use a set of compasses to draw its graph.
   
   
   
3. To translate this circle 5 units to the left, subtract 5 from the x-coordinate of its centre to get -3. To translate the circle 4 units up, add 4 to the y-coordinate of its centre to get 1. The centre of the translated circle is thus (-3 , 1). The radius is unaffected. So the equation of the translated circle is:
   ( x + 3)² + (y - 1)² = 25