Question

(07.01 HC)Prove that the two circles shown below are similar.Circle B is shown with a center at negative 1, 5 and a radius of 4. Circle D is shown with a center of 7, 4 and a radius of 2.

Answer 1

Step-by-step explanation:

From the information given,

Circle B has center(- 1, 5) and r = 4

Circle D has center(7, 4) and r = 2

Step 1

Translate circle B to circle D such that they have the same center point. We would translate circle B 8 units to the left and 1 unit upwards.

Step 2

We would dilate circle D so that it has same size as circle B. We would find the scale factor . By comparing their radii,

scale factor = radius of B/radius of D = 4/2 = 2

This means that by multiplying circle D by 2, we have two circles with the same radius and center point.

Thus, after using translation and dilation to map Circle D to B, we can conclude that that circle B and D are similar