Question

In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of ? Use the distance formula to help you decide

Answer 1

Original coordinates of the points:
A (8,15) ; B (12,13) ; C (8,10)

Dilated scale factor of 3.

A ⇒ 3x = 3(8) = 24 ; 3y = 3(15) = 45 ⇒ A' (24,45)
B ⇒ 3x = 3(12) = 36 ; 3y = 3(13) = 39 ⇒ B' (36, 39)
C ⇒ 3x = 3(8) = 24 ; 3y = 3(10) = 30 ⇒ C' (24, 30)

The given image forms a right triangle. So, I'll get the short leg and long leg of the right triangle to solve for the hypotenuse, length of CB.

Short leg: y value of B and C
39 - 30 = 9

Long leg: x value of B and C
36 - 24 = 12

a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c²
√225 = √c²
15 = c

The length of CB is 15 units.