Under an enlargement centre(2,1)the image p(1,1)is p'(4,5).determine the scale factor of the enlargement
To determine the scale factor of an enlargement, we need to find the ratio of corresponding lengths. In this case, we can use the distance formula to find the distance between the center of enlargement and the point, and the distance between the image and the center of enlargement:
Distance between center of enlargement and point P(1,1)
= sqrt((1-2)^2 + (1-1)^2)
= sqrt(1)
= 1
Distance between center of enlargement and image P'(4,5)
= sqrt((4-2)^2 + (5-1)^2)
= sqrt(20)
= 2sqrt(5)
Thus, the scale factor is the ratio of the distances:
(2sqrt(5)) / 1
= 2sqrt(5)
Therefore, the scale factor of the enlargement is 2sqrt(5).